Year 6 Coordinates, Reflection and Translation: check-up and SATs-style questions

Key words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.

Method. Read the across number first, then the up or down number, from the origin for point P.

1. Start at the origin. The origin is (0, 0), where the two axes cross.
   (0, 0)
2. Read the across number first. Move across along the x-axis. Move left if the number is negative.
   x = −3
3. Read the up or down number. Move up along the y-axis. Move down if the number is negative.
   y = 2
4. Write the coordinates. Always write the across number first, then the up or down number.
   (-3, 2)

Check. Check on the grid: the point is 3 squares left of the y-axis, and it is 2 squares up from the x-axis. ✓

Watch out. Across is always the first number. Do not swap the two numbers.

Key words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.

Method. Use the signs of the two numbers to find the quadrant.

1. Look at the across number. Positive means right of the y-axis. Negative means left of it.
   x = −7, so left of the y-axis
2. Look at the up or down number. Positive means above the x-axis. Negative means below it.
   y = −1, so below the x-axis
3. Name the quadrant. The quadrants go round anticlockwise, starting at the top right.
   third quadrant

Check. The first quadrant is top right, the second is top left, the third is bottom left and the fourth is bottom right. ✓

Watch out. Look at the signs, not the size of the numbers. Two negative signs make the third quadrant.

Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.

Method. Move the across number first, then the up or down number, one move at a time.

1. Start at the point. Write the across number and the up or down number of the point.
   start = (4, -2)
2. Move across first. Moving 3 squares left changes the across number. Take away 3.
   x: 4 − 3 = 1
3. Move up or down. Moving 5 squares up changes the up or down number. Add 5.
   y: −2 + 5 = 3
4. Write the new point. Write the across number first, then the up or down number.
   (1, 3)

Check. Move back 3 squares right and 5 squares down and you return to (4, -2). ✓

Watch out. Moving left or down takes away from the number. Moving right or up adds to it.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides. In this chapter the mirror lines are the axes.

Method. Flip the point over the mirror line. It stays the same distance from the mirror line, on the other side.

1. Write the point. Write its across number and its up or down number.
   (-5, 3)
2. Look at the mirror line. The mirror line is the x-axis. The point flips over it, so the across number does not change.
   x stays −5
3. Flip the up or down number. The point is 3 squares above the x-axis. Its image is the same distance below it.
   y: 3 becomes −3
4. Write the image. Write the across number first, then the up or down number.
   (-5, -3)

Check. (-5, -3) is 3 squares below the x-axis, the same distance as (-5, 3) is above it. ✓

Watch out. Reflecting in the x-axis changes the up or down number, not the across number.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides. In this chapter the mirror lines are the axes.

Method. Flip the point over the mirror line. It stays the same distance from the mirror line, on the other side.

1. Write the point. Write its across number and its up or down number.
   (6, -2)
2. Look at the mirror line. The mirror line is the y-axis. The point flips over it, so the up or down number does not change.
   y stays −2
3. Flip the across number. The point is 6 squares right of the y-axis. Its image is the same distance left of it.
   x: 6 becomes −6
4. Write the image. Write the across number first, then the up or down number.
   (-6, -2)

Check. (-6, -2) is 6 squares left of the y-axis, the same distance as (6, -2) is right of it. ✓

Watch out. Reflecting in the y-axis changes the across number, not the up or down number.

Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.

Method. Use the two sides you can see to find the corner that completes the rectangle.

1. Find the horizontal side. (2, 1) and (-4, 1) have the same up or down number, so they are joined by a side across the grid.
   up or down number = 1
2. Find the vertical side. (2, 1) and (2, 5) have the same across number, so they are joined by a side up or down the grid.
   across number = 2
3. Find the missing corner. It takes the across number of (-4, 1) and the up or down number of (2, 5).
   across −4, up or down 5
4. Write the answer. The fourth corner completes the rectangle.
   (-4, 5)

Check. (2, 1), (-4, 1), (-4, 5) and (2, 5) make a rectangle, with opposite sides the same length. ✓

Watch out. Do not copy one of the corners you were given. The missing corner is a new point.

Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.

Method. Compare where the point started with where it ended, one number at a time.

1. Compare the across numbers. Work out how far the across number changed.
   −3 to 2: 5 squares right
2. Compare the up or down numbers. Work out how far the up or down number changed.
   −2 to 4: 6 squares up
3. Write the translation. Say the across move first, then the up or down move.
   5 squares right and 6 squares up

Check. Start at (-3, -2) and move 5 squares right and 6 squares up: you reach (2, 4). ✓

Watch out. Say the across move first. A move with no across part is not a move to the right or left.

Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.

Method. Count the squares along the side, using only the numbers that change.

1. Find the numbers that change. The two points have the same up or down number, so the side runs across.
   −6 and −1
2. Find the length. The two points are on the same side of the axis, so take the smaller distance away from the bigger one.
   6 − 1 = 5
3. Write the answer. A length is never negative.
   5

Check. Count the squares from (-6, 3) to (-1, 3) one at a time: there are 5. ✓

Watch out. When the side crosses an axis, add the two distances from the axis. Do not subtract them.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides. In this chapter the mirror lines are the axes.

Method. Reflect the image back over the mirror line. Reflecting again gives the original point, because it is the same distance from the mirror line.

1. Write the point. Write its across number and its up or down number.
   (4, -3)
2. Look at the mirror line. The mirror line is the y-axis. The point flips over it, so the up or down number does not change.
   y stays −3
3. Flip the across number. The point is 4 squares right of the y-axis. Its image is the same distance left of it.
   x: 4 becomes −4
4. Write the image. Write the across number first, then the up or down number.
   (-4, -3)

Check. (-4, -3) is 4 squares left of the y-axis, the same distance as (4, -3) is right of it. ✓

Watch out. Reflecting in the y-axis changes the across number, not the up or down number.

Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.

Method. Do the moves one at a time, in the order they are given.

1. Start with the point. Write its coordinates before any move.
   (-2, 1)
2. Move 1: translate 3 squares right and 2 squares down. Every corner moves the same number of squares, so both numbers change by the move.
   (-2, 1) to (1, -1)
   x: −2 + 3 = 1; y: 1 − 2 = −1
3. Move 2: reflect in the x-axis. The mirror line is the x-axis, so only the up or down number changes sign.
   (1, -1) to (1, 1)
   y: −1 becomes 1
4. Write the final point. Write across first, then up or down.
   (1, 1)

Check. Each move was checked with the number that changed. The final point is (1, 1). ✓

Watch out. Do the moves in the order they are given. Reflecting and then translating can give a different answer from translating and then reflecting.

Key words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.

Method. Read the across number first, then the up or down number, from the origin for point T.

1. Start at the origin. The origin is (0, 0), where the two axes cross.
   (0, 0)
2. Read the across number first. Move across along the x-axis. Move left if the number is negative.
   x = −3
3. Read the up or down number. Move up along the y-axis. Move down if the number is negative.
   y = −4
4. Write the coordinates. Always write the across number first, then the up or down number.
   (-3, -4)

Check. Check on the grid: the point is 3 squares left of the y-axis, and it is 4 squares down from the x-axis. ✓

Watch out. Across is always the first number. Do not swap the two numbers.

Key words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.

Method. Compare the signs of each point with the quadrant you need.

1. Check the signs of each point. Look at the across number and the up or down number of every point in turn.
   (3, 4): + across, + up or down   (-2, 5): - across, + up or down   (-4, -1): - across, - up or down
2. Find the point with the right signs. The point (-2, 5) has the signs that put it in the second quadrant.
   (-2, 5) is in the second quadrant
3. Write the point. Write the across number first, then the up or down number.
   (-2, 5)

Check. (-2, 5) has a negative across number and a positive up or down number. ✓

Watch out. Look at the signs first. Do not choose a point just because its numbers look bigger.

Key words. A reflection flips a shape over a mirror line. Each point and its image are the same distance from the mirror line, on opposite sides. In this chapter the mirror lines are the axes.

Method. Flip the point over the mirror line. It stays the same distance from the mirror line, on the other side.

1. Write the point. Write its across number and its up or down number.
   (-1, 6)
2. Look at the mirror line. The mirror line is the x-axis. The point flips over it, so the across number does not change.
   x stays −1
3. Flip the up or down number. The point is 6 squares above the x-axis. Its image is the same distance below it.
   y: 6 becomes −6
4. Write the image. Write the across number first, then the up or down number.
   (-1, -6)

Check. (-1, -6) is 6 squares below the x-axis, the same distance as (-1, 6) is above it. ✓

Watch out. Reflecting in the x-axis changes the up or down number, not the across number.

Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.

Method. Move the across number first, then the up or down number, one move at a time.

1. Start at the point. Write the across number and the up or down number of corner M.
   start = (-2, 4)
2. Move across first. Moving 4 squares right changes the across number. Add 4.
   x: −2 + 4 = 2
3. Move up or down. Moving 3 squares down changes the up or down number. Take away 3.
   y: 4 − 3 = 1
4. Write the new point. Write the across number first, then the up or down number.
   (2, 1)

Check. Move back 4 squares left and 3 squares up and you return to (-2, 4). ✓

Watch out. Moving left or down takes away from the number. Moving right or up adds to it.

Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.

Method. Use the two sides you can see to find the corner that completes the rectangle.

1. Find the horizontal side. (-1, -3) and (-6, -3) have the same up or down number, so they are joined by a side across the grid.
   up or down number = −3
2. Find the vertical side. (-1, -3) and (-1, 2) have the same across number, so they are joined by a side up or down the grid.
   across number = −1
3. Find the missing corner. It takes the across number of (-6, -3) and the up or down number of (-1, 2).
   across −6, up or down 2
4. Write the answer. The fourth corner completes the rectangle.
   (-6, 2)

Check. (-1, -3), (-6, -3), (-6, 2) and (-1, 2) make a rectangle, with opposite sides the same length. ✓

Watch out. Do not copy one of the corners you were given. The missing corner is a new point.

Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.

Method. Do the moves one at a time, in the order they are given.

1. Start with the point. Write its coordinates before any move.
   (3, -2)
2. Move 1: reflect in the y-axis. The mirror line is the y-axis, so only the across number changes sign.
   (3, -2) to (-3, -2)
   x: 3 becomes −3
3. Move 2: translate 5 squares down. Every corner moves the same number of squares, so both numbers change by the move.
   (-3, -2) to (-3, -7)
   x: −3 + 0 = −3; y: −2 − 5 = −7
4. Write the final point. Write across first, then up or down.
   (-3, -7)

Check. Each move was checked with the number that changed. The final point is (-3, -7). ✓

Watch out. Do the moves in the order they are given. Reflecting and then translating can give a different answer from translating and then reflecting.