Year 6: Reflecting in the y-axis
Part of the Year 6 coordinates, reflection and translation chapter. Chapter overview · whole chapter on one page
Reflecting in the y-axis
The mirror line in this section is the y-axis, which goes up and down the grid. Each point and its image are the same distance from the y-axis, on opposite sides.
When a point is reflected in the y-axis, its up or down number stays the same. Its across number changes sign. So (4, 2) becomes (-4, 2), and (-5, -3) becomes (5, -3).
A shape that crosses the y-axis is reflected as well. Reflect each corner, then join the new corners in the same order.
Key ideas
- Reflecting in the y-axis keeps the up or down number and changes the sign of the across number.
- The point and its image are the same distance from the y-axis, on opposite sides.
- A point on the y-axis, with an across number of 0, does not move.
- A reflection keeps the size and shape of the shape.
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.
- Write the point. Write its across number and its up or down number.(4, 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
- 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
- Write the image. Write the across number first, then the up or down number.(-4, 2)
Check. (-4, 2) is 4 squares left of the y-axis, the same distance as (4, 2) is right of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(-5, -3)
- 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
- Flip the across number. The point is 5 squares left of the y-axis. Its image is the same distance right of it.x: −5 becomes 5
- Write the image. Write the across number first, then the up or down number.(5, -3)
Check. (5, -3) is 5 squares right of the y-axis, the same distance as (-5, -3) is left of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(3, 1)
- 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 1
- Flip the across number. The point is 3 squares right of the y-axis. Its image is the same distance left of it.x: 3 becomes −3
- Write the image. Write the across number first, then the up or down number.(-3, 1)
Check. (-3, 1) is 3 squares left of the y-axis, the same distance as (3, 1) is right of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down number.
Watch out
Common mistake: changing the up or down number when reflecting in the y-axis. The point (4, 2) becomes (-4, 2): only the across number changes sign. Also, remember that the image is on the other side of the y-axis, the same distance away.
Exercise 11E Practice: reflecting points in the y-axis
Non-calculatorKey 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.
- Write the point. Write its across number and its up or down number.(3, 5)
- 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 5
- Flip the across number. The point is 3 squares right of the y-axis. Its image is the same distance left of it.x: 3 becomes −3
- Write the image. Write the across number first, then the up or down number.(-3, 5)
Check. (-3, 5) is 3 squares left of the y-axis, the same distance as (3, 5) is right of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(-6, 1)
- 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 1
- Flip the across number. The point is 6 squares left of the y-axis. Its image is the same distance right of it.x: −6 becomes 6
- Write the image. Write the across number first, then the up or down number.(6, 1)
Check. (6, 1) is 6 squares right of the y-axis, the same distance as (-6, 1) is left of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(2, -4)
- 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 −4
- Flip the across number. The point is 2 squares right of the y-axis. Its image is the same distance left of it.x: 2 becomes −2
- Write the image. Write the across number first, then the up or down number.(-2, -4)
Check. (-2, -4) is 2 squares left of the y-axis, the same distance as (2, -4) is right of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(-1, -7)
- 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 −7
- Flip the across number. The point is 1 squares left of the y-axis. Its image is the same distance right of it.x: −1 becomes 1
- Write the image. Write the across number first, then the up or down number.(1, -7)
Check. (1, -7) is 1 squares right of the y-axis, the same distance as (-1, -7) is left of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(1, 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
- Flip the across number. The point is 1 squares right of the y-axis. Its image is the same distance left of it.x: 1 becomes −1
- Write the image. Write the across number first, then the up or down number.(-1, 2)
Check. (-1, 2) is 1 squares left of the y-axis, the same distance as (1, 2) is right of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(-3, 4)
- 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 4
- Flip the across number. The point is 3 squares left of the y-axis. Its image is the same distance right of it.x: −3 becomes 3
- Write the image. Write the across number first, then the up or down number.(3, 4)
Check. (3, 4) is 3 squares right of the y-axis, the same distance as (-3, 4) is left of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(5, -1)
- 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 −1
- Flip the across number. The point is 5 squares right of the y-axis. Its image is the same distance left of it.x: 5 becomes −5
- Write the image. Write the across number first, then the up or down number.(-5, -1)
Check. (-5, -1) is 5 squares left of the y-axis, the same distance as (5, -1) is right of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(-2, 1)
- 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 1
- Flip the across number. The point is 2 squares left of the y-axis. Its image is the same distance right of it.x: −2 becomes 2
- Write the image. Write the across number first, then the up or down number.(2, 1)
Check. (2, 1) is 2 squares right of the y-axis, the same distance as (-2, 1) is left of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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.
- Write the point. Write its across number and its up or down number.(-4, -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
- Flip the across number. The point is 4 squares left of the y-axis. Its image is the same distance right of it.x: −4 becomes 4
- Write the image. Write the across number first, then the up or down number.(4, -2)
Check. (4, -2) is 4 squares right of the y-axis, the same distance as (-4, -2) is left 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.
- Start with the point. Write its coordinates before any move.(3, -5)
- Move 1: reflect in the y-axis. The mirror line is the y-axis, so only the across number changes sign.(3, -5) to (-3, -5)
x: 3 becomes −3 - Move 2: translate 4 squares left. Every corner moves the same number of squares, so both numbers change by the move.(-3, -5) to (-7, -5)
x: −3 − 4 = −7; y: −5 + 0 = −5 - Write the final point. Write across first, then up or down.(-7, -5)
Check. Each move was checked with the number that changed. The final point is (-7, -5). ✓
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. 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.
- Write the point. Write its across number and its up or down number.(-2, 6)
- 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 6
- Flip the across number. The point is 2 squares left of the y-axis. Its image is the same distance right of it.x: −2 becomes 2
- Write the image. Write the across number first, then the up or down number.(2, 6)
Check. (2, 6) is 2 squares right of the y-axis, the same distance as (-2, 6) is left of it. ✓
Watch out. Reflecting in the y-axis changes the across number, not the up or down 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. Think about what the y-axis does to a point that is already on it.
- Look at the point. The point (0, 4) has an across number of 0. It is on the y-axis.x = 0
- Reflect it. Changing the sign of 0 gives 0 again, so the image is in the same place.-0 = 0
- Decide. Ruby is right, because a point on the mirror line does not move.Yes
Check. (0, 4) reflects to (0, 4). ✓
Watch out. A point on the mirror line is its own image.
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. Compare the across numbers and the up or down numbers of the point and its image.
- Compare the up or down numbers. Both points are 2 squares up, so the up or down numbers are the same.y = 2 for both
- Compare the across numbers. The across numbers are opposite: -5 and 5.-5 and 5 are opposite
- Decide. The mirror line is halfway between the two points, and it is the y-axis.the y-axis
Check. (-5, 2) and (5, 2) are both 5 squares from the y-axis, on opposite sides. ✓
Watch out. Where the across numbers change sign and the up or down number stays the same, the mirror line is the y-axis.
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. Work through the two reflections for P = (-3, 2), then name the quadrant of the final point.
- Reflect P in the y-axis. The across number changes sign, and the up or down number stays the same.(-3, 2) becomes (3, 2)
- Reflect Q in the x-axis. The across number stays the same, and the up or down number changes sign.(3, 2) becomes (3, -2)
- Name the quadrant of R. Positive across and negative up or down: right and below the origin.fourth quadrant
Check. Any point in the second quadrant gives the same answer. The final point, (3, -2), is in the fourth quadrant. ✓
Watch out. Two reflections change both signs. Check the sign of each number after every step.