Year 4 Coordinates and Translation: check-up and SATs-style questions

Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.

Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.

1. Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.
   (0, 0)
2. Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.
   P is above the number 2 on the x-axis.
   Along = 2
3. Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.
   P is level with the number 5 on the y-axis.
   Up = 5
4. Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.
   P = (2, 5)

Check. Start at (0, 0). Go 2 along and 5 up. You arrive at P. ✓

Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.

Key words. To plot a point means to mark it on a grid with a small cross or dot. A vertex is a corner of a shape (more than one are called vertices). A polygon is a flat shape with straight sides.

Method. Start at the origin. For each point go along first, then up, and mark it with a cross.

1. Find the origin. Every point is measured from (0, 0), where the axes meet.
   Put your finger on (0, 0).
2. Plot A (4, 3). The first number is along, the second number is up. Then mark the point with a small cross.
   Go 4 along the x-axis, then 3 up.
3. Check the picture. Every point should sit where its along number and up number meet.

Check. Read each point back: look along to its x-coordinate and up to its y-coordinate. They match the numbers in the question. ✓

Watch out. Do not mix up the two numbers: along first, then up.

Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.

Method. Start at the origin. Go along first, then up. The letter you land on is the answer.

1. Start at the origin. Every position is measured from the point (0, 0).
   (0, 0)
2. Go 5 along the x-axis. The first number is the along number.
   (5, 2): along = 5
3. Go 2 up. The second number is the up number.
   Up = 2
4. Read the letter at the point. We stop where the two moves meet.
   The letter is B.

Check. Point B is 5 along and 2 up, which is (5, 2). ✓

Watch out. Do not go up first. The first number is always the along number.

Key words. A vertex is a corner of a shape. Horizontal means flat, like the horizon. Vertical means straight up and down. A parallelogram has two pairs of parallel sides. A kite has two pairs of equal sides that are next to each other.

Method. A rectangle has sides that go straight across and straight up. The missing corner lines up with one corner going up or down, and with another corner going across.

1. Write the coordinates of the corners you know. We use them to work out the missing corner.
   A = (1, 2)
   B = (6, 2)
   C = (6, 5)
2. Find the side joining D to A. In a rectangle the sides are straight up and down or flat. AD goes straight up or down, so D has the same x-coordinate as A.
   A = (1, 2), so the x-coordinate of D is 1.
3. Find the side joining D to C. CD is a flat side, so D has the same y-coordinate as C.
   C = (6, 5), so the y-coordinate of D is 5.
4. Write the missing corner and draw the sides. Put the x-coordinate first, then the y-coordinate. Join it to the other corners.
   D = (1, 5)

Check. The completed shape is a rectangle. ✓

Watch out. Check each side of your shape. It must look like the shape in the question.

Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.

Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).

1. Write the starting point. Along first, then up.
   A = (3, 4)
2. Move 2 squares right. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.
   x: 3 + 2 = 5
3. Move 3 squares up. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.
   y: 4 + 3 = 7
4. Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.
   A′ = (5, 7)

Check. Count on the grid from (3, 4): 2 right, 3 up gets to (5, 7). ✓

Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.

Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.

Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.

1. Write the two points. Along first, then up.
   A = (2, 5) and B = (6, 2)
2. Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.
   x goes from 2 to 6: 6 − 2 = 4
   4 right
3. Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.
   y goes from 5 to 2: 5 − 2 = 3
   3 down
4. Write the translation. We say the left or right move first, then the up or down move.
   From A to B: 4 right, 3 down

Check. Start at (2, 5) and move 4 right, 3 down: you get to (6, 2). ✓

Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).

Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.

Method. Translate every corner by the same move. Then join the new corners in the same order.

1. Write the corners of the shape. We move every corner (vertex) by the same move.
   A = (3, 3)
   B = (5, 3)
   C = (3, 5)
2. Move every corner 2 left, 1 down. Right adds to x, left takes away from x. Up adds to y, down takes away from y.
   A (3, 3) → (3 − 2, 3 − 1) = A′ (1, 2)
   B (5, 3) → (5 − 2, 3 − 1) = B′ (3, 2)
   C (3, 5) → (3 − 2, 5 − 1) = C′ (1, 4)
3. Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
4. Write the new coordinates. The new shape has the same size and shape as the old one.
   A′ (1, 2), B′ (3, 2), C′ (1, 4)

Check. Each new corner is 2 left, 1 down from the old one, and the new shape looks the same as the old shape. ✓

Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.

Key words. A grid reference tells you which square of a map something is in. We say the letter (along the bottom) first, then the number (up the side). The compass points are North (N), East (E), South (S) and West (W), and in between them NE, SE, SW and NW.

Method. Look down to the letter along the bottom. Look across to the number up the side. Write the letter first, then the number.

1. Find the place on the map. Look for the shop.
   The shop is in the square that is highlighted.
2. Read the letter. The letters are along the bottom of the map. Look straight down from the square. The letter comes first.
   Letter = E
3. Read the number. The numbers are up the side of the map. Look straight across from the square.
   Number = 4
4. Write the grid reference. Letter first, then number, with no space or comma.
   E4

Check. Start at E along the bottom and go up to row 4: you reach the shop. ✓

Watch out. The letter comes first. E3 is not the same as 3E.

Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.

Method. Follow the instructions one at a time. F means forward, R means turn right (a quarter turn) and L means turn left (a quarter turn). Write the position after each instruction.

1. Write the start point and the way the robot faces. We follow the program from here. The robot’s left and right depend on the way it is facing.
   Start at (2, 1), facing north.
2. Instruction 1: F2. Forward 2 squares north.
   (2, 1) → (2, 3)
3. Instruction 2: R. Turn right a quarter turn: now facing east.
   north → east
4. Instruction 3: F3. Forward 3 squares east.
   (2, 3) → (5, 3)
5. Write where the robot finishes. Look at the last position and the last way it faces.
   The robot ends at (5, 3), facing east.

Check. Draw the path on the grid from (2, 1): it ends at (5, 3). ✓

Watch out. Turn left or right from the way the robot is facing, not from the way you are looking at the page.

Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.

Method. Read the point carefully, along first and then up. Compare with Ben’s answer.

1. Read the point P. Look down to the x-axis, then across to the y-axis.
   P is above 3 and level with 5.
2. Write the coordinates. Along first, then up.
   P = (3, 5)
3. Compare. Ben wrote (5, 3). That is 5 along and 3 up.
   Ben is wrong: he wrote the up number first.

Check. (3, 5) means 3 along and 5 up. ✓

Watch out. Along first, then up.

Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.

Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.

1. Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.
   (0, 0)
2. Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.
   A is above the number 5 on the x-axis.
   Along = 5
3. Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.
   A is level with the number 3 on the y-axis.
   Up = 3
4. Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.
   A = (5, 3)

Check. Start at (0, 0). Go 5 along and 3 up. You arrive at A. ✓

Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.

Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.

Method. Start at the origin. Go along first, then up. The letter you land on is the answer.

1. Start at the origin. Every position is measured from the point (0, 0).
   (0, 0)
2. Go 2 along the x-axis. The first number is the along number.
   (2, 6): along = 2
3. Go 6 up. The second number is the up number.
   Up = 6
4. Read the letter at the point. We stop where the two moves meet.
   The letter is X.

Check. Point X is 2 along and 6 up, which is (2, 6). ✓

Watch out. Do not go up first. The first number is always the along number.

Key words. A vertex is a corner of a shape. Horizontal means flat, like the horizon. Vertical means straight up and down. A parallelogram has two pairs of parallel sides. A kite has two pairs of equal sides that are next to each other.

Method. Plot the three points. A rectangle has straight sides across and up, so D lines up with A and with C.

1. Plot A, B and C. Along first, then up.
   A (1, 1): 1 along, 1 up
   B (4, 1): 4 along, 1 up
   C (4, 3): 4 along, 3 up
2. Find D. D is straight above A (x = 1) and level with C (y = 3).
   D = (1, 3)
3. Draw the shape. Join A, B, C, D in order.

Check. The sides are 3 and 2 long, with 4 right angles. It is a rectangle. ✓

Watch out. D copies the x from A and the y from C.

Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.

Method. Translate every corner by the same move. Then join the new corners in the same order.

1. Write the corners of the shape. We move every corner (vertex) by the same move.
   A = (1, 2)
   B = (3, 2)
   C = (1, 5)
2. Move every corner 3 right, 2 up. Right adds to x, left takes away from x. Up adds to y, down takes away from y.
   A (1, 2) → (1 + 3, 2 + 2) = A′ (4, 4)
   B (3, 2) → (3 + 3, 2 + 2) = B′ (6, 4)
   C (1, 5) → (1 + 3, 5 + 2) = C′ (4, 7)
3. Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
4. Write the new coordinates. The new shape has the same size and shape as the old one.
   A′ (4, 4), B′ (6, 4), C′ (4, 7)

Check. Each new corner is 3 right, 2 up from the old one, and the new shape looks the same as the old shape. ✓

Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.

Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.

Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.

1. Write the two points. Along first, then up.
   A = (2, 4) and B = (7, 2)
2. Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.
   x goes from 2 to 7: 7 − 2 = 5
   5 right
3. Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.
   y goes from 4 to 2: 4 − 2 = 2
   2 down
4. Write the translation. We say the left or right move first, then the up or down move.
   From A to B: 5 right, 2 down

Check. Start at (2, 4) and move 5 right, 2 down: you get to (7, 2). ✓

Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).

Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.

Method. Follow the instructions one at a time. F means forward, R means turn right (a quarter turn) and L means turn left (a quarter turn). Write the position after each instruction.

1. Write the start point and the way the robot faces. We follow the program from here. The robot’s left and right depend on the way it is facing.
   Start at (3, 2), facing east.
2. Instruction 1: F2. Forward 2 squares east.
   (3, 2) → (5, 2)
3. Instruction 2: L. Turn left a quarter turn: now facing north.
   east → north
4. Instruction 3: F3. Forward 3 squares north.
   (5, 2) → (5, 5)
5. Instruction 4: L. Turn left a quarter turn: now facing west.
   north → west
6. Instruction 5: F4. Forward 4 squares west.
   (5, 5) → (1, 5)
7. Write where the robot finishes. Look at the last position and the last way it faces.
   The robot ends at (1, 5), facing west.

Check. Draw the path on the grid from (3, 2): it ends at (1, 5). ✓

Watch out. Turn left or right from the way the robot is facing, not from the way you are looking at the page.

Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.

Method. Look at the second number. A point on the x-axis has a second number of 0.

1. Look at the point. The point is (4, 0): 4 along and 0 up.
   x = 4, y = 0
2. Find where it is. It has not gone up at all, so it is on the bottom line, the x-axis.
   It is on the x-axis.
3. Answer. Points on the y-axis have x = 0.
   Amira is wrong. (4, 0) is on the x-axis.

Check. The y-axis points are like (0, 4), with 0 along. ✓

Watch out. A point on the x-axis has y = 0. A point on the y-axis has x = 0.

Key words. A vertex is a corner of a shape. Horizontal means flat, like the horizon. Vertical means straight up and down. A parallelogram has two pairs of parallel sides. A kite has two pairs of equal sides that are next to each other.

Method. Find the missing corner D of the parallelogram. Then find the move from A to B.

1. Find the move from B to C. In a parallelogram opposite sides make the same move.
   B (5, 1) to C (6, 4): 1 right, 3 up.
2. Do the same move from A. Add 1 to x and 3 to y.
   A (1, 1) → D (1 + 1, 1 + 3) = (2, 4)
3. Find the move from A to B. Compare the coordinates.
   A (1, 1) to B (5, 1): x goes up 4, y does not change.
   The move is 4 right.

Check. ABCD has two pairs of parallel sides: it is a parallelogram. ✓

Watch out. Use the same move for the opposite side.

Key words. A program is a list of instructions. Forward means go straight ahead. A turn left or right is a quarter turn (a right angle) unless it says half turn. A half turn is two quarter turns.

Method. Follow the three directions one at a time. Then compare the start and the treasure to find the one move.

1. Follow the directions. East makes x bigger. North makes y bigger. West makes x smaller.
   4 east: (2, 3) → (6, 3)
   2 north: (6, 3) → (6, 5)
   3 west: (6, 5) → (3, 5)
2. Write the treasure. The last point is the treasure.
   The treasure is at (3, 5).
3. Find the one move from the start. Compare (2, 3) and (3, 5).
   x: 2 to 3 is 1 right.
   y: 3 to 5 is 2 up.
   The move is 1 right, 2 up.

Check. 4 east then 3 west is 1 east. Then 2 north. ✓

Watch out. West takes away from x. Do not add it.