Websink Prep UKKS2 Maths reasoning (SATs)Year 6 chaptersMaths reasoning (SATs) textbooksYear 6Browse allPast papersFind a tutorBecome a tutor
SATs practice · Year 6Chapter 6 · Position and coordinates
Year 6 · Chapter 6

Position and coordinates

By the end of this chapter you will be able to

  • Read and write the coordinates of a point in any quadrant
  • Translate a shape by a given move and write the new coordinates
  • Reflect a shape in the x-axis, the y-axis or a line such as x = 3
  • Find a missing corner or the centre of a rectangle from its coordinates
  • Follow and give compass directions and quarter turns

You should already know

  • Coordinates in the first quadrant (Year 5 geometry)
  • Negative numbers on a number line (Chapter 1 of this book)

Where this leads

  • Measures in context (Chapter 4 of this book) and statistics (Chapter 8 of this book)

KS2 SATs practice for reasoning (Year 6). Original questions in the style of the national tests. Content: Describe positions on a full coordinate grid with all four quadrants (Year 6), Draw and translate simple shapes on a coordinate plane (Year 6), Reflect shapes in the axes and in lines such as x = 3 (Year 6), Identify, describe and represent the position of a shape after a reflection or translation, and know that the shape has not changed (Year 5-6), Find missing coordinates of vertices of a shape and of a shape's centre (Year 6), Solve problems with compass directions and turns, and use the language of position to give and follow instructions (Year 5-6).

Exercise P  Do you remember?

Non-calculator
1
FWork out 2 - 5.
2
FWhich is larger: -1 or -4?
3
FWhat are the coordinates of the origin?
4
FHow many quarter turns make one full turn?
5
FWork out 3 + 4 x 2 - 1.
6.1

Coordinates in four quadrants

Year 6
Describe positions on a full coordinate grid with all four quadrants (Year 6)
Video lesson: Coordinates in four quadrantsComing soon
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. A treasure map has a grid with the origin in the middle. The pirate says the chest is at (-3, 2), which is left of the middle and above it. Mia must plot the point in the right quadrant.

Rule

The grid has an x-axis (across) and a y-axis (up and down). Points are written (x, y), x first.

The quadrants go anticlockwise from the top right: first (+, +), second (-, +), third (-, -), fourth (+, -).

Key ideas

  • x first, then y: (3, -2) is 3 right and 2 down.
  • First quadrant: both positive. Third quadrant: both negative.
  • A point on an axis is in no quadrant.
-5-5-4-4-3-3-2-2-1-11122334455
A triangle on a coordinate grid.
Worked example 6.1.1
Write the coordinates of the top vertex of the triangle in the picture.

Method. The top vertex is the highest point; read x first, then y.

  1. Read x. The vertex is 2 steps right of the y-axis.
    x = 2
  2. Read y. It is 5 steps up from the x-axis.
    y = 5
  3. Write the point. Write x first, then y.
    (2, 5)
  4. Write the answer.
    (2, 5)

Check. (2, 5): 2 right and 5 up. ✓

Worked example 6.1.2
The point (-3, 2) is in which quadrant? Write first, second, third or fourth.

Method. Look at the signs of the x- and y-coordinates.

  1. Look at the sign of x. x = -3, which is negative.
    x < 0
  2. Look at the sign of y. y = 2, which is positive.
    y > 0
  3. Name the quadrant. x is negative and y is positive, so the point is in the second quadrant.
    second
  4. Write the answer.
    second

Check. Quadrant 1 is ++, 2 is -+, 3 is --, 4 is +-. ✓

Watch out. Quadrants go anticlockwise from the top right: first, second, third, fourth.

Worked example 6.1.3
The point (-2, -4) is in which quadrant? Write first, second, third or fourth.

Method. Look at the signs of the x- and y-coordinates.

  1. Look at the sign of x. x = -2, which is negative.
    x < 0
  2. Look at the sign of y. y = -4, which is negative.
    y < 0
  3. Name the quadrant. x is negative and y is negative, so the point is in the third quadrant.
    third
  4. Write the answer.
    third

Check. Quadrant 1 is ++, 2 is -+, 3 is --, 4 is +-. ✓

Watch out. Quadrants go anticlockwise from the top right: first, second, third, fourth.

Watch out

Watch out. Always write x first. (3, -2) and (-2, 3) are different points.

Exam tip

Practice guide. Count from the origin: across first, then up or down.

Exercise 6A  Practice: four quadrants and reading points

Non-calculator
1
FThe point (4, 5) is in which quadrant? Write first, second, third or fourth.
2
FThe point (-6, 1) is in which quadrant? Write first, second, third or fourth.
3
FThe point (-2, -7) is in which quadrant? Write first, second, third or fourth.
4
FThe point (5, -3) is in which quadrant? Write first, second, third or fourth.
5
FWhat are the coordinates of the point 3 squares to the left of the origin and 4 squares down?
6
FWhich point is (-3, 4)? Choose one: (-3, 4), (4, -3) or (3, -4).
7
FTick the points that are in the second quadrant. Options: (-2, 3) | (2, 3) | (-2, -3) | (-5, 1). Write the options you would tick, in the order given.
8
PSHow many units apart are the points (-2, 3) and (-2, -4)? Write the number.
9
PSA treasure map starts at (-2, -1). The pirate moves up 5 squares. What are the new coordinates?
10
RExplain why the point (0, 5) is not in any quadrant.
11
RSam says that (-3, -3) and (3, 3) are reflections of each other in the x-axis. Is he right? Write yes or no.
12
FWrite the coordinates of the vertices of this triangle, starting at the bottom left and going anticlockwise.
-5-5-4-4-3-3-2-2-1-11122334455
13
FA point is 5 squares right of the y-axis and 2 squares below the x-axis. Write its coordinates.
14
RBen plots the points (4, 3), (-4, 3), (-4, -3) and (4, -3). What shape do they make, and is it a square or a rectangle? Write square or rectangle.
6.2

Translating shapes

Year 6
Draw and translate simple shapes on a coordinate plane (Year 6), Identify, describe and represent the position of a shape after a translation, and know that the shape has not changed (Year 5-6)
Video lesson: Translating shapesComing soon
Story. A robot on a school carpet grid slides a square tile 3 squares right and 2 squares up. The tile is still the same tile, just in a new place.

Rule

A translation slides a shape without turning or flipping it. Every point moves the same distance in the same direction.

To translate, add the move to each coordinate: a move of 2 right and 3 down is (x + 2, y - 3).

Key ideas

  • Translation: add the move to x and y.
  • The size and shape of the shape stay the same.
  • Right and up are positive; left and down are negative.
-5-5-4-4-3-3-2-2-1-11122334455
The triangle before a translation.
Worked example 6.2.1
Shape A has vertices (1, 1), (3, 1), (1, 4). It is translated 2 right and 3 down. Write the coordinates of its new vertices in the same order.

Method. Add the move to the x-coordinate and the y-coordinate of each vertex.

  1. Read the move. Every vertex moves 2 right and 3 down.
    add 2 to x and -3 to y
  2. Move each vertex. Add the move to each coordinate pair.
    (1, 1) -> (3, -2) ; (3, 1) -> (5, -2) ; (1, 4) -> (3, 1)
  3. Write the new coordinates. The shape has the same size and shape, only its position changes.
    (3, -2), (5, -2), (3, 1)
  4. Write the answer.
    (3, -2), (5, -2), (3, 1)

Check. Each new point is 2 right and 3 down from the old one. ✓

Watch out. A translation slides the shape. Its size and shape stay the same.

Worked example 6.2.2
Shape B has vertices (-4, 2), (-2, 2), (-4, 5). It is translated 5 right. Write the coordinates of its new vertices in the same order.

Method. Add the move to the x-coordinate and the y-coordinate of each vertex.

  1. Read the move. Every vertex moves 5 right.
    add 5 to x and 0 to y
  2. Move each vertex. Add the move to each coordinate pair.
    (-4, 2) -> (1, 2) ; (-2, 2) -> (3, 2) ; (-4, 5) -> (1, 5)
  3. Write the new coordinates. The shape has the same size and shape, only its position changes.
    (1, 2), (3, 2), (1, 5)
  4. Write the answer.
    (1, 2), (3, 2), (1, 5)

Check. Each new point is 5 right from the old one. ✓

Watch out. A translation slides the shape. Its size and shape stay the same.

Worked example 6.2.3
A shape has a vertex at (2, 2). After a translation it is at (7, -1). Describe the move.

Method. Find the change in x and in y.

  1. Change in x. 7 - 2 = 5, so 5 right.
    +5
  2. Change in y. -1 - 2 = -3, so 3 down.
    -3
  3. Describe the move. The move is 5 right and 3 down.
    5 right and 3 down
  4. Write the answer.
    5 right and 3 down

Check. 2 + 5 = 7 and 2 - 3 = -1. ✓

Watch out

Watch out. A translation does not turn or flip the shape. If the shape is turned, it is not just a translation.

Exam tip

Practice guide. Move one vertex first, check it is in the right place, then move the others the same way.

Exercise 6B  Practice: translating shapes

Non-calculator
1
FShape C has vertices (0, 0), (2, 0), (2, 3), (0, 3). It is translated 3 right and 1 down. Write the coordinates of its new vertices in the same order.
2
FShape D has vertices (-3, 2), (-1, 2), (-2, 5). It is translated 4 right. Write the coordinates of its new vertices in the same order.
3
FShape E has vertices (-4, -4), (-2, -4), (-4, -1). It is translated 5 right and 3 up. Write the coordinates of its new vertices in the same order.
4
FShape F has vertices (1, -2), (4, -2), (4, -5). It is translated 6 left and 4 up. Write the coordinates of its new vertices in the same order.
5
PSShape G has vertices (2, 1), (5, 1), (5, 4), (2, 4). It is translated 3 left and 3 down. Write the coordinates of its new vertices in the same order.
6
PSA point moves from (-1, 3) to (2, -1). Describe the move.
7
PSWhich translation moves (-1, 3) to (2, -1)? Choose one: 3 right and 4 down, 3 left and 4 up or 3 right and 4 up.
8
RTick the statements that are true about a translation. Options: The shape keeps its size | The shape is turned | Each point moves the same distance in the same direction | The shape is flipped. Write the options you would tick, in the order given.
9
RAli says that a translation changes the size of a shape. Is he right? Explain.
10
FA square has corners (1, 1), (3, 1), (3, 3) and (1, 3). It is translated 4 left. Write the new coordinate of the corner at (3, 3).
11
PSShape H has vertices (-5, 0), (-3, 0), (-3, 2). It is translated 2 right and 2 down. Write the coordinates of its new vertices in the same order.
12
RDescribe how to move the triangle with corners (1, 1), (3, 1) and (1, 4) so that its bottom left corner is at the origin.
6.3

Reflecting shapes in axes and lines

Year 6
Reflect shapes in the axes and in lines such as x = 3 (Year 6)
Video lesson: Reflecting shapes in axes and linesComing soon
Story. Ruth folds a paper flag along a line so that one half lies exactly on the other. The fold is a mirror line, and each point on one side has a matching point the same distance away on the other side.

Rule

A reflection flips a shape over a mirror line. Each point is the same distance from the line as its image, on the other side.

In the x-axis, the sign of y changes: (x, y) becomes (x, -y). In the y-axis, the sign of x changes: (x, y) becomes (-x, y). In the line x = k, x becomes 2k - x.

Key ideas

  • Reflection in the x-axis: (x, y) -> (x, -y).
  • Reflection in the y-axis: (x, y) -> (-x, y).
  • Reflection in x = 3: x -> 6 - x.
-5-5-4-4-3-3-2-2-1-11122334455
A triangle to reflect in the x-axis.
Worked example 6.3.1
Shape B has vertices (1, 2), (3, 2), (2, 4). It is reflected in the x-axis. Write the new coordinates in the same order.

Method. Reflecting in the x-axis: change the sign of y.

  1. Find the rule for the x-axis. Reflecting in the x-axis means you change the sign of y.
    change the sign of y
  2. Apply the rule to each vertex. Each point moves to the same distance on the other side.
    (1, 2) -> (1, -2) ; (3, 2) -> (3, -2) ; (2, 4) -> (2, -4)
  3. Write the new vertices. Keep the vertices in the same order.
    (1, -2), (3, -2), (2, -4)
  4. Write the answer.
    (1, -2), (3, -2), (2, -4)

Check. Each point is the same distance from the mirror line. ✓

Watch out. Points on the mirror line do not move.

Worked example 6.3.2
Shape C has vertices (1, 1), (2, 3), (4, 1). It is reflected in the line x = 3. Write the new coordinates in the same order.

Method. Reflecting in x = 3: x becomes 2 x 3 - x, and y stays the same.

  1. Find the rule for x = 3. Each x moves to 2 x 3 - x, so the same distance is kept on the other side.
    x -> 2 x 3 - x
  2. Apply the rule. Keep the y-coordinate the same.
    (1, 1) -> (5, 1) ; (2, 3) -> (4, 3) ; (4, 1) -> (2, 1)
  3. Write the new vertices. Keep the vertices in the same order.
    (5, 1), (4, 3), (2, 1)
  4. Write the answer.
    (5, 1), (4, 3), (2, 1)

Check. Each point is the same distance from x = 3. ✓

Watch out. Check one point: its distance to the line before and after must be the same.

Worked example 6.3.3
The point (3, 4) is reflected in the y-axis. Write the new point.

Method. In the y-axis, the sign of x changes.

  1. Change the sign of x. x = 3 becomes -3.
    x = -3
  2. Keep y. y stays the same, so y = 4.
    (-3, 4)
  3. Write the answer.
    (-3, 4)

Check. (-3, 4) is the same distance from the y-axis. ✓

Watch out

Watch out. When reflecting in x = 3, do not just change the sign. The point (2, 5) goes to (4, 5), because it is 1 unit left of the line.

Exam tip

Practice guide. Count the squares from the mirror line to each point, then count the same number on the other side.

Exercise 6C  Practice: reflections

Non-calculator
1
FShape D has vertices (2, 1), (4, 1), (4, 3). It is reflected in the x-axis. Write the new coordinates in the same order.
2
FShape E has vertices (-3, 2), (-1, 4), (-1, 1). It is reflected in the y-axis. Write the new coordinates in the same order.
3
FShape F has vertices (0, 0), (1, 2), (2, 0). It is reflected in the line x = 3. Write the new coordinates in the same order.
4
FShape G has vertices (4, 1), (5, 4), (6, 1). It is reflected in the line x = 3. Write the new coordinates in the same order.
5
PSShape H has vertices (-4, -1), (-2, -1), (-2, -4), (-4, -4). It is reflected in the x-axis. Write the new coordinates in the same order.
6
FReflect the point (2, 5) in the line x = 3. Write the new point.
7
FWhich point is the reflection of (3, 4) in the y-axis? Choose one: (-3, 4), (3, -4) or (-3, -4).
8
RTick the statements that are true about reflections. Options: A point on the mirror line does not move | A reflection changes the size of the shape | Reflection in the x-axis changes the sign of y | Reflection in the y-axis changes the sign of y. Write the options you would tick, in the order given.
9
RAli says that a point (2, 2) and its reflection in the x-axis are the same distance from the x-axis. Is he right? Write yes or no.
10
RExplain why the point (3, 0) does not move when it is reflected in the x-axis.
11
PSShape J has vertices (1, 1), (3, 1), (3, 4), (1, 4). It is reflected in the line x = 4. Write the new coordinates in the same order.
6.4

Missing coordinates and the centre of a shape

Year 6
Find missing coordinates of vertices of a shape and of a shape's centre (Year 6)
Video lesson: Missing coordinates and the centre of a shapeComing soon
Story. A school designer has marked three corners of a rectangular playground on a plan. She must find the fourth corner, and the centre of the playground where the flagpole goes.

Rule

The centre of a rectangle is halfway between two opposite corners: add the two x-values and halve; do the same for y.

If a rectangle has sides parallel to the axes, the missing corner uses the x-value and the y-value that appear only once.

Key ideas

  • Centre = halfway between opposite corners.
  • Halve the sum of the coordinates.
  • Missing corner: the x-value and y-value that appear once.
Worked example 6.4.1
The opposite corners of rectangle PQRS are (1, 1) and (5, 3). What are the coordinates of its centre?

Method. The centre is halfway between opposite corners.

  1. Add the x-coordinates of the opposite corners. 1 + 5 = 6.
    6
  2. Halve it. 6 / 2 = 3.
    x = 3
  3. Do the same for the y-coordinates. 1 + 3 = 4, and half of that is 2.
    (3, 2)
  4. Write the answer.
    (3, 2)

Check. The centre is halfway between (1, 1) and (5, 3). ✓

Watch out. Halve the sum of the coordinates, not the difference.

Worked example 6.4.2
Three corners of rectangle T are (1, 2), (5, 2) and (1, 6). The sides are parallel to the axes. What are the coordinates of the fourth corner?

Method. Find the x-value and the y-value that appear only once.

  1. Look at the x-coordinates. The x-coordinates are 1, 5 and 1. One of them is the only one that appears once.
    x = 5
  2. Look at the y-coordinates. The y-coordinates are 2, 2 and 6.
    y = 6
  3. Write the fourth corner. The fourth corner uses the unpaired x and y values.
    (5, 6)
  4. Write the answer.
    (5, 6)

Check. The corners (1, 2), (5, 2), (1, 6) and (5, 6) make a rectangle. ✓

Watch out. The fourth corner shares its x with one corner and its y with another.

Worked example 6.4.3
The opposite corners of rectangle UVWX are (-4, -2) and (2, 6). What are the coordinates of its centre?

Method. The centre is halfway between opposite corners.

  1. Add the x-coordinates of the opposite corners. -4 + 2 = -2.
    -2
  2. Halve it. -2 / 2 = -1.
    x = -1
  3. Do the same for the y-coordinates. -2 + 6 = 4, and half of that is 2.
    (-1, 2)
  4. Write the answer.
    (-1, 2)

Check. The centre is halfway between (-4, -2) and (2, 6). ✓

Watch out. Halve the sum of the coordinates, not the difference.

Watch out

Watch out. The centre is the midpoint, not the difference. Add the coordinates, then halve.

Exam tip

Practice guide. Sketch the rectangle quickly on squared paper. The missing corner is then easy to see.

Exercise 6D  Practice: missing corners and centres

Non-calculator
1
FThe opposite corners of rectangle ABCD are (0, 0) and (6, 4). What are the coordinates of its centre?
2
FThe opposite corners of rectangle EFGH are (-2, 1) and (4, 5). What are the coordinates of its centre?
3
FThe opposite corners of rectangle IJKL are (-6, -4) and (2, 0). What are the coordinates of its centre?
4
FThree corners of rectangle M are (2, 1), (6, 1) and (2, 5). The sides are parallel to the axes. What are the coordinates of the fourth corner?
5
FThree corners of rectangle N are (-3, -2), (-3, 4) and (1, 4). The sides are parallel to the axes. What are the coordinates of the fourth corner?
6
FThree corners of rectangle P are (0, 0), (5, 0) and (5, 3). The sides are parallel to the axes. What are the coordinates of the fourth corner?
7
PSThe centre of a square is (3, 3). One corner is (1, 1). What are the coordinates of the opposite corner?
8
PSA rectangle has corners at (0, 0) and (8, 6) at opposite ends of a diagonal. What is the centre? Write the coordinates.
9
RExplain how to find the centre of a rectangle with corners (-2, 3) and (4, -1).
10
PSThree corners of a rectangle are (-1, 2), (3, 2) and (3, -4). Find the fourth corner.
11
RA square has corners (0, 0), (4, 0) and (4, 4). Explain why its centre is (2, 2).
12
FA rectangle has corners (1, 1), (7, 1), (7, 5) and (1, 5). Write the coordinates of its centre.
-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-11122334455667788
13
PSThree corners of rectangle Q are (-4, -4), (-4, 2) and (3, 2). The sides are parallel to the axes. What are the coordinates of the fourth corner?
6.5

Compass directions, turns and instructions

Year 6
Solve problems with compass directions and turns, and use the language of position to give and follow instructions (Year 5-6)
Video lesson: Compass directions, turns and instructionsComing soon
Story. A school trip leader gives directions to the coach driver: "Face north, turn right, go 3 squares east, then turn left and go 2 squares north." Each turn is a quarter turn, which is a right angle.

Rule

The compass directions in order, going clockwise, are North, East, South, West.

A quarter turn clockwise moves one step along that list; anticlockwise moves one step back.

Key ideas

  • Clockwise: North, East, South, West, then back to North.
  • A quarter turn is a right angle; four quarter turns make a full turn.
  • Give instructions in a clear order: direction, then distance.
Worked example 6.5.1
You are facing North. You turn 1 quarter turn(s) clockwise. Which direction are you facing now?

Method. Use the compass order North, East, South, West.

  1. Put the directions in order. Clockwise from North: North, East, South, West.
    North -> East -> South -> West
  2. Turn 1 quarter turn(s) clockwise. Start at North and move 1 place(s) along the list.
    North -> East
  3. Write the answer.
    East

Check. Four quarter turns bring you back to North. ✓

Watch out. A right angle is a quarter turn. Turning clockwise goes North, East, South, West.

Worked example 6.5.2
You are facing West. You turn 1 quarter turn(s) anticlockwise. Which direction are you facing now?

Method. Use the compass order North, East, South, West.

  1. Put the directions in order. Clockwise from North: North, East, South, West.
    North -> East -> South -> West
  2. Turn 1 quarter turn(s) anticlockwise. Start at West and move 1 place(s) along the list.
    West -> South
  3. Write the answer.
    South

Check. Four quarter turns bring you back to West. ✓

Watch out. A right angle is a quarter turn. Turning clockwise goes North, East, South, West.

Worked example 6.5.3
You are facing East. You turn 3 quarter turn(s) clockwise. Which direction are you facing now?

Method. Use the compass order North, East, South, West.

  1. Put the directions in order. Clockwise from North: North, East, South, West.
    North -> East -> South -> West
  2. Turn 3 quarter turn(s) clockwise. Start at East and move 3 place(s) along the list.
    East -> North
  3. Write the answer.
    North

Check. Four quarter turns bring you back to East. ✓

Watch out. A right angle is a quarter turn. Turning clockwise goes North, East, South, West.

Watch out

Watch out. After West, a clockwise turn gives North, not South. Check the order each time.

Exam tip

Practice guide. Draw the four compass points on a small circle, then move your finger round the turns.

Exercise 6E  Practice: compass directions and instructions

Non-calculator
1
FYou are facing South. You turn 2 quarter turn(s) clockwise. Which direction are you facing now?
2
FYou are facing East. You turn 2 quarter turn(s) anticlockwise. Which direction are you facing now?
3
FYou are facing North. You turn 4 quarter turn(s) clockwise. Which direction are you facing now?
4
PSYou are facing South. You turn 3 quarter turn(s) anticlockwise. Which direction are you facing now?
5
PSA robot starts at (1, 1). It moves 3 squares right and then 2 squares up. What are its new coordinates?
6
FWhich words describe a 90 degree turn? Choose one: a half turn, a quarter turn or a full turn.
7
FYou face North. You make a half turn. Which direction are you facing? Write the word.
8
RGive an instruction to walk from the school gate to the library, which is 4 squares east and 2 squares north of the gate.
9
FA pupil faces East and makes a quarter turn anticlockwise. Which direction is she now facing? Write the word.
10
RA map has the library at (0, 0). The park is at (-3, 2). Write which two directions from the library you walk to reach the park, and the distance in squares each way. Give your answer as: west 3, north 2.
11
RTick the instructions that take you from (0, 0) to (3, -2). Options: 3 right and 2 up | 3 right and 2 down | 2 right and 3 down | 3 left and 2 down. Write the options you would tick, in the order given.
12
PSShape K has vertices (-1, 0), (1, 0), (0, 2). It is translated 3 right and 2 down. Write the coordinates of its new vertices in the same order.
13
RExplain why turning clockwise four times returns you to the same direction.

Chapter summary

SkillMethod
CoordinatesWrite (x, y): x across first, then y up or down.
QuadrantsFirst (+, +), second (-, +), third (-, -), fourth (+, -), anticlockwise.
TranslationAdd the move to each coordinate. The shape keeps its size and shape.
Reflection in the x-axis(x, y) becomes (x, -y).
Reflection in the y-axis(x, y) becomes (-x, y).
Reflection in x = kx becomes 2k - x; y stays the same.
Centre of a rectangleHalfway between opposite corners: halve the sums of the coordinates.
CompassClockwise: North, East, South, West. A quarter turn is a right angle.

Can you…?

  • I can read and write coordinates in all four quadrants
  • I can translate a shape and write its new coordinates
  • I can reflect a shape in the x-axis, the y-axis and a line such as x = 3
  • I can find a missing corner or the centre of a rectangle
  • I can follow and give compass directions and quarter turns

Key terms

origin
the point (0, 0) where the x-axis and y-axis cross
quadrant
one of the four parts of a coordinate grid
translation
a slide of a shape, with no turn or flip
reflection
a flip of a shape over a mirror line
mirror line
the line a shape is reflected in
quarter turn
a turn of 90 degrees, which is a right angle

Exercise 6Z  Check-up

Non-calculator
1
The point (-1, -6) is in which quadrant? Write first, second, third or fourth.
2
Shape L has vertices (2, 2), (4, 2), (4, 5). It is translated 3 left and 1 up. Write the coordinates of its new vertices in the same order.
3
Shape M has vertices (1, 3), (3, 3), (3, 6). It is reflected in the y-axis. Write the new coordinates in the same order.
4
Shape N has vertices (0, 1), (1, 4), (2, 1). It is reflected in the line x = 3. Write the new coordinates in the same order.
5
The opposite corners of rectangle PQRS are (-2, 0) and (6, 4). What are the coordinates of its centre?
6
Three corners of rectangle T are (1, 1), (7, 1) and (7, 4). The sides are parallel to the axes. What are the coordinates of the fourth corner?
7
You are facing West. You turn 3 quarter turn(s) clockwise. Which direction are you facing now?
8
A point is at (-5, 4). It is translated 6 right and 2 down. Write its new coordinates.
9
Explain why a reflection in the y-axis of the point (4, -2) is (-4, -2).
10
The point (7, -9) is in which quadrant? Write first, second, third or fourth.

Total 19 marks. Allow about 19 minutes.

Exercise 6X  Practice test questions

Non-calculator
1
FThe point (-8, 3) is in which quadrant? Write first, second, third or fourth.[1 mark]
2
PSShape Z has vertices (0, 0), (3, 0), (3, 2). It is translated 1 right and 4 down. Write the coordinates of its new vertices in the same order.[2 marks]
3
PSShape Y has vertices (2, 3), (5, 3), (5, 6). It is reflected in the x-axis. Write the new coordinates in the same order.[2 marks]
4
PSShape X has vertices (1, 2), (2, 4), (3, 2). It is reflected in the line x = 3. Write the new coordinates in the same order.[2 marks]
5
PSThe opposite corners of rectangle WXYZ are (-6, 2) and (4, 8). What are the coordinates of its centre?[2 marks]
6
PSThree corners of rectangle V are (3, -1), (3, 5) and (9, 5). The sides are parallel to the axes. What are the coordinates of the fourth corner?[2 marks]
7
FYou are facing North. You turn 1 quarter turn(s) anticlockwise. Which direction are you facing now?[1 mark]
8
PSA dog starts at (2, -3) and runs 4 squares left and 5 squares up. Where does it stop? Write the coordinates.[2 marks]
9
RExplain in words how you would reflect the point (-2, 5) in the x-axis.[3 marks]
10
PSA rectangle has corners (0, 0), (6, 0) and (6, 4). Write the coordinates of the fourth corner.[2 marks]
← Chapter 5: Geometry: angles and shapesChapter 7: Algebra and sequences →

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings