Year 6: Reflecting in the x-axis
Part of the Year 6 coordinates, reflection and translation chapter. Chapter overview · whole chapter on one page
Reflecting in the x-axis
A reflection flips a shape over a mirror line. The mirror line in this section is the x-axis, which goes across the grid. Each point and its image are the same distance from the x-axis, on opposite sides.
When a point is reflected in the x-axis, its across number stays the same. Its up or down number changes sign. So (3, 4) becomes (3, -4), and (-2, -5) becomes (-2, 5).
A point that is on the x-axis, with an up or down number of 0, does not move.
Key ideas
- Reflecting in the x-axis keeps the across number and changes the sign of the up or down number.
- The point and its image are the same distance from the x-axis, on opposite sides.
- A point on the x-axis does not move when it is reflected in the x-axis.
- The shape keeps its size and shape. Only its position changes.
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 x-axis. The point flips over it, so the across number does not change.x stays 3
- Flip the up or down number. The point is 4 squares above the x-axis. Its image is the same distance below it.y: 4 becomes −4
- Write the image. Write the across number first, then the up or down number.(3, -4)
Check. (3, -4) is 4 squares below the x-axis, the same distance as (3, 4) 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.
- Write the point. Write its across number and its up or down number.(-2, -5)
- 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 −2
- Flip the up or down number. The point is 5 squares below the x-axis. Its image is the same distance above it.y: −5 becomes 5
- Write the image. Write the across number first, then the up or down number.(-2, 5)
Check. (-2, 5) is 5 squares above the x-axis, the same distance as (-2, -5) is below 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. Reflect the image back over the mirror line. Reflecting again gives the original point, because it is the same distance from the mirror line.
- Write the point. Write its across number and its up or down number.(5, -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
- Flip the up or down number. The point is 2 squares below the x-axis. Its image is the same distance above it.y: −2 becomes 2
- Write the image. Write the across number first, then the up or down number.(5, 2)
Check. (5, 2) is 2 squares above the x-axis, the same distance as (5, -2) is below it. ✓
Watch out. Reflecting in the x-axis changes the up or down number, not the across number.
Watch out
Common mistake: changing the across number when reflecting in the x-axis. The point (3, 4) becomes (3, -4), not (-3, 4). Only the sign of the up or down number changes.
Exercise 11D Practice: reflecting points in the x-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.(2, 6)
- 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 2
- 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
- Write the image. Write the across number first, then the up or down number.(2, -6)
Check. (2, -6) is 6 squares below the x-axis, the same distance as (2, 6) 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.
- Write the point. Write its across number and its up or down number.(-4, 3)
- 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 −4
- 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
- Write the image. Write the across number first, then the up or down number.(-4, -3)
Check. (-4, -3) is 3 squares below the x-axis, the same distance as (-4, 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.
- 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 x-axis. The point flips over it, so the across number does not change.x stays 5
- Flip the up or down number. The point is 1 squares below the x-axis. Its image is the same distance above it.y: −1 becomes 1
- Write the image. Write the across number first, then the up or down number.(5, 1)
Check. (5, 1) is 1 squares above the x-axis, the same distance as (5, -1) is below 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.
- Write the point. Write its across number and its up or down number.(-7, -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 −7
- Flip the up or down number. The point is 2 squares below the x-axis. Its image is the same distance above it.y: −2 becomes 2
- Write the image. Write the across number first, then the up or down number.(-7, 2)
Check. (-7, 2) is 2 squares above the x-axis, the same distance as (-7, -2) is below 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.
- Write the point. Write its across number and its up or down number.(1, 3)
- 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
- 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
- Write the image. Write the across number first, then the up or down number.(1, -3)
Check. (1, -3) is 3 squares below the x-axis, the same distance as (1, 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.
- Write the point. Write its across number and its up or down number.(4, 1)
- 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 4
- Flip the up or down number. The point is 1 squares above the x-axis. Its image is the same distance below it.y: 1 becomes −1
- Write the image. Write the across number first, then the up or down number.(4, -1)
Check. (4, -1) is 1 squares below the x-axis, the same distance as (4, 1) 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.
- Write the point. Write its across number and its up or down number.(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 3
- Flip the up or down number. The point is 2 squares below the x-axis. Its image is the same distance above it.y: −2 becomes 2
- Write the image. Write the across number first, then the up or down number.(3, 2)
Check. (3, 2) is 2 squares above the x-axis, the same distance as (3, -2) is below 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.
- Write the point. Write its across number and its up or down number.(4, 5)
- 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 4
- Flip the up or down number. The point is 5 squares above the x-axis. Its image is the same distance below it.y: 5 becomes −5
- Write the image. Write the across number first, then the up or down number.(4, -5)
Check. (4, -5) is 5 squares below the x-axis, the same distance as (4, 5) 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.
- 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 x-axis. The point flips over it, so the across number does not change.x stays 3
- Flip the up or down number. The point is 5 squares below the x-axis. Its image is the same distance above it.y: −5 becomes 5
- Write the image. Write the across number first, then the up or down number.(3, 5)
Check. (3, 5) is 5 squares above the x-axis, the same distance as (3, -5) is below it. ✓
Watch out. Reflecting in the x-axis changes the up or down number, not the across 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. Count the squares along the side, using only the numbers that change.
- Find the numbers that change. The two points have the same across number, so the side runs up or down.2 and −2
- Find the length. The two points are on opposite sides of the x-axis, so add how far each one is from the x-axis.2 + 2 = 4
- Write the answer. A length is never negative.4
Check. Count the squares from (-4, 2) to (-4, -2) one at a time: there are 4. ✓
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. 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, 5)
- 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 2
- Flip the up or down number. The point is 5 squares above the x-axis. Its image is the same distance below it.y: 5 becomes −5
- Write the image. Write the across number first, then the up or down number.(2, -5)
Check. (2, -5) is 5 squares below the x-axis, the same distance as (2, 5) 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. Think about what the x-axis does to a point that is already on it.
- Look at the point. The point (3, 0) has an up or down number of 0. It is on the x-axis.y = 0
- Reflect it. Changing the sign of 0 gives 0 again, so the image is in the same place.-0 = 0
- Decide. Sam is right, because a point on the mirror line does not move.Yes
Check. (3, 0) reflects to (3, 0). ✓
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. 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 x-axis. The point flips over it, so the across number does not change.x stays −1
- Flip the up or down number. The point is 2 squares above the x-axis. Its image is the same distance below it.y: 2 becomes −2
- Write the image. Write the across number first, then the up or down number.(-1, -2)
Check. (-1, -2) is 2 squares below the x-axis, the same distance as (-1, 2) 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. P is 5 squares left of the y-axis and 3 squares below the x-axis. Reflect it in the x-axis: the across number stays, and the up or down number changes sign.
- 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 x-axis. The point flips over it, so the across number does not change.x stays −5
- Flip the up or down number. The point is 3 squares below the x-axis. Its image is the same distance above it.y: −3 becomes 3
- Write the image. Write the across number first, then the up or down number.(-5, 3)
Check. (-5, 3) is 3 squares above the x-axis, the same distance as (-5, -3) is below it. ✓
Watch out. Reflecting in the x-axis changes the up or down number, not the across number.