Year 6 Maths reasoning (SATs) Position and coordinates: check-up and practice test questions

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

1. Look at the sign of x. x = -1, which is negative.
   x < 0
2. Look at the sign of y. y = -6, 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.

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

1. Read the move. Every vertex moves 3 left and 1 up.
   add -3 to x and 1 to y
2. Move each vertex. Add the move to each coordinate pair.
   (2, 2) -> (-1, 3) ; (4, 2) -> (1, 3) ; (4, 5) -> (1, 6)
3. Write the new coordinates. The shape has the same size and shape, only its position changes.
   (-1, 3), (1, 3), (1, 6)
4. Write the answer.
   (-1, 3), (1, 3), (1, 6)

Check. Each new point is 3 left and 1 up from the old one. ✓

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

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

1. Find the rule for the y-axis. Reflecting in the y-axis means you change the sign of x.
   change the sign of x
2. Apply the rule to each vertex. Each point moves to the same distance on the other side.
   (1, 3) -> (-1, 3) ; (3, 3) -> (-3, 3) ; (3, 6) -> (-3, 6)
3. Write the new vertices. Keep the vertices in the same order.
   (-1, 3), (-3, 3), (-3, 6)
4. Write the answer.
   (-1, 3), (-3, 3), (-3, 6)

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

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

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.
   (0, 1) -> (6, 1) ; (1, 4) -> (5, 4) ; (2, 1) -> (4, 1)
3. Write the new vertices. Keep the vertices in the same order.
   (6, 1), (5, 4), (4, 1)
4. Write the answer.
   (6, 1), (5, 4), (4, 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.

Method. The centre is halfway between opposite corners.

1. Add the x-coordinates of the opposite corners. -2 + 6 = 4.
   4
2. Halve it. 4 / 2 = 2.
   x = 2
3. Do the same for the y-coordinates. 0 + 4 = 4, and half of that is 2.
   (2, 2)
4. Write the answer.
   (2, 2)

Check. The centre is halfway between (-2, 0) and (6, 4). ✓

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

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

1. Look at the x-coordinates. The x-coordinates are 1, 7 and 7. One of them is the only one that appears once.
   x = 1
2. Look at the y-coordinates. The y-coordinates are 1, 1 and 4.
   y = 4
3. Write the fourth corner. The fourth corner uses the unpaired x and y values.
   (1, 4)
4. Write the answer.
   (1, 4)

Check. The corners (1, 1), (7, 1), (7, 4) and (1, 4) make a rectangle. ✓

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

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 West and move 3 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.

Method. Add 6 to x and subtract 2 from y.

1. x. -5 + 6 = 1.
   1
2. y. 4 - 2 = 2.
   2
3. Write the answer.
   (1, 2)

Check. (1 - 6, 2 + 2) = (-5, 4). ✓

Method. Keep y and change x.

1. Change the sign of x. 4 becomes -4.
   -4
2. Keep y. y = -2 stays the same.
   (-4, -2)
3. Write the answer.
   Because a reflection in the y-axis changes the sign of x and keeps y the same.

Check. (-4, -2) is the same distance from the y-axis. ✓

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

1. Look at the sign of x. x = 7, which is positive.
   x > 0
2. Look at the sign of y. y = -9, which is negative.
   y < 0
3. Name the quadrant. x is positive and y is negative, so the point is in the fourth quadrant.
   fourth
4. Write the answer.
   fourth

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

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

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

1. Look at the sign of x. x = -8, which is negative.
   x < 0
2. Look at the sign of y. y = 3, 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.

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

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

Check. Each new point is 1 right and 4 down from the old one. ✓

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

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.
   (2, 3) -> (2, -3) ; (5, 3) -> (5, -3) ; (5, 6) -> (5, -6)
3. Write the new vertices. Keep the vertices in the same order.
   (2, -3), (5, -3), (5, -6)
4. Write the answer.
   (2, -3), (5, -3), (5, -6)

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

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

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, 2) -> (5, 2) ; (2, 4) -> (4, 4) ; (3, 2) -> (3, 2)
3. Write the new vertices. Keep the vertices in the same order.
   (5, 2), (4, 4), (3, 2)
4. Write the answer.
   (5, 2), (4, 4), (3, 2)

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.

Method. The centre is halfway between opposite corners.

1. Add the x-coordinates of the opposite corners. -6 + 4 = -2.
   -2
2. Halve it. -2 / 2 = -1.
   x = -1
3. Do the same for the y-coordinates. 2 + 8 = 10, and half of that is 5.
   (-1, 5)
4. Write the answer.
   (-1, 5)

Check. The centre is halfway between (-6, 2) and (4, 8). ✓

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

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

1. Look at the x-coordinates. The x-coordinates are 3, 3 and 9. One of them is the only one that appears once.
   x = 9
2. Look at the y-coordinates. The y-coordinates are -1, 5 and 5.
   y = -1
3. Write the fourth corner. The fourth corner uses the unpaired x and y values.
   (9, -1)
4. Write the answer.
   (9, -1)

Check. The corners (3, -1), (3, 5), (9, 5) and (9, -1) make a rectangle. ✓

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

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 North and move 1 place(s) along the list.
   North -> West
3. Write the answer.
   West

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.

Method. Subtract 4 from x and add 5 to y.

1. x. 2 - 4 = -2.
   -2
2. y. -3 + 5 = 2.
   2
3. Write the answer.
   (-2, 2)

Check. (-2 + 4, 2 - 5) = (2, -3). ✓

Method. Think about which coordinate changes sign.

1. Keep x. x = -2 stays the same.
   -2
2. Change y. y = 5 becomes -5, so the point is (-2, -5).
   (-2, -5)
3. Write the answer.
   Keep the x-coordinate the same and change the sign of y, so the point becomes (-2, -5).

Check. Changing the sign of y gives -5. ✓

Method. The fourth corner shares x with one corner and y with another.

1. x. x-values: 0, 6, 6. The one that appears once is 0.
   0
2. y. y-values: 0, 0, 4. The one that appears once is 4.
   4
3. Write the answer.
   (0, 4)

Check. The rectangle has corners (0, 0), (6, 0), (6, 4) and (0, 4). ✓