Year 5: Drawing reflections and finding the mirror line
Part of the Year 5 reflection and translation chapter. Chapter overview · whole chapter on one page
Drawing reflections and finding the mirror line
To draw a reflection, take each corner in turn. Count the squares from the corner to the mirror line. Then count the same number of squares on the other side, and put a dot. Join the dots in the same order as the original shape.
If you know a point and its image, the mirror line is halfway between them.
Key ideas
- Count the squares from each corner to the mirror line, then the same number on the other side.
- The mirror line is halfway between a point and its image.
- The image has the same size and shape, and faces the other way.
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.
Method. Count the squares from the point to the mirror line, then count the same number on the other side.
- Find the mirror line. The dashed red line is the mirror line.the dashed red line
- Count the squares from the point to the line. The point is 5 squares left the line.5 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.5 squares right the line
- Write the answer. 5 squares to the right of the mirror line
Check. The point and its image are both 5 squares from the line. ✓
Watch out. The image is on the other side of the line, not on the same side.
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.
Method. The mirror line is halfway between the point and its image.
- Add the two distances from the edge. The point is 2 squares from the edge, and its image is 8 squares from the edge.2 + 8 = 10
- Halve the total. The mirror line is in the middle, so halve the total.10 ÷ 2 = 5
- Write the answer. the mirror line is 5 squares from the left edge
Check. From the line, 5 − 2 = 3 and 8 − 5 = 3, the same distance. ✓
Watch out. Check the answer: the distance on both sides must be the same.
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.
Method. Count the distance to the mirror line, then count the same distance on the other side.
- Find the mirror line. The mirror line is 3 squares from the bottom edge.mirror line at 3
- Count the squares from the point to the line. The point is 1 square from the line.1 squares
- Count the same number on the other side. The image is the same distance from the line, on the other side.3 − 1 = 2
- Write the answer. 2 squares from the bottom edge
Check. The point and its image are both 1 squares from the line. ✓
Watch out. Count from the bottom edge every time, so you do not mix up the two sides.
Watch out
A common mistake is to draw the image the wrong distance from the line, for example one square too close. Count the squares from the line for each corner, and then count the same number on the other side.
Exercise 10D Drawing reflections and finding the mirror line
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.
Method. Count the squares from A' to the mirror line. The image is the same distance on the other side.
- Find the mirror line. The dashed red line is 6 squares from the left edge.line at 6
- Find the image corner. A' is 11 squares from the left edge.A' at 11
- Count the squares from A' to the line. Subtract the line from the image corner.11 − 6 = 5
- Write the answer. 5 squares
Check. A is 5 squares from the line too: 6 − 1 = 5. ✓
Watch out. Count from the image to the line. Its distance matches the original.
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.
Method. Count the squares from corner B to the mirror line, then find the image corner the same distance above the line.
- Find B. Corner B is at the bottom right of the blue rectangle, 3 squares below the mirror line.B is 3 below
- Find the image corner. The image corner is 3 squares above the line.B is at 5, the line is at 8
- Check the image corner. B' is at the top right of the orange rectangle, and it is 11 squares up from the bottom.B' at 11
- Write the answer. It is 11 minus the line at 8, so it is 3 squares above the line.11 − 8 = 3 B'
Check. B is 3 squares below the line, and B' is 3 squares above it. ✓
Watch out. Check the other side of the line, not the same side.
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.
Method. Count the distance to the mirror line, then count the same distance on the other side.
- Find the mirror line. The mirror line is 5 squares from the left edge.mirror line at 5
- Count the squares from the point to the line. The point is 1 square from the line.1 squares
- Count the same number on the other side. The image is the same distance from the line, on the other side.5 + 1 = 6
- Write the answer. 6 squares from the left edge
Check. The point and its image are both 1 squares from the line. ✓
Watch out. Count from the left edge every time, so you do not mix up the two sides.
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.
Method. Count the distance to the mirror line, then count the same distance on the other side.
- Find the mirror line. The mirror line is 5 squares from the left edge.mirror line at 5
- Count the squares from the point to the line. The point is 3 squares from the line.3 squares
- Count the same number on the other side. The image is the same distance from the line, on the other side.5 + 3 = 8
- Write the answer. 8 squares from the left edge
Check. The point and its image are both 3 squares from the line. ✓
Watch out. Count from the left edge every time, so you do not mix up the two sides.
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.
Method. Count the distance to the mirror line, then count the same distance on the other side.
- Find the mirror line. The mirror line is 5 squares from the left edge.mirror line at 5
- Count the squares from the point to the line. The point is 2 squares from the line.2 squares
- Count the same number on the other side. The image is the same distance from the line, on the other side.5 − 2 = 3
- Write the answer. 3 squares from the left edge
Check. The point and its image are both 2 squares from the line. ✓
Watch out. Count from the left edge every time, so you do not mix up the two sides.
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.
Method. Draw the image on the other side of the line, one corner at a time.
- Find the mirror line. The dashed red line is 5 squares from the left edge.line at 5
- Reflect each corner. Each corner is the same distance from the line on the other side.corners move across the line
- Measure the width of the image. A reflection keeps the same size and shape, so the width does not change.3 squares wide
- Write the answer. 3 squares
Check. The original L is 3 squares wide, and the image is too. ✓
Watch out. A reflection never changes the width of a 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.
Method. Count the distance to the mirror line, then count the same distance on the other side.
- Find the mirror line. The mirror line is 4 squares from the bottom edge.mirror line at 4
- Count the squares from the point to the line. The point is 2 squares from the line.2 squares
- Count the same number on the other side. The image is the same distance from the line, on the other side.4 − 2 = 2
- Write the answer. 2 squares from the bottom edge
Check. The point and its image are both 2 squares from the line. ✓
Watch out. Count from the bottom edge every time, so you do not mix up the two sides.
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.
Method. Find the distance from the edge to the point, then to the line.
- Find the total. The point is 2 squares from the bottom and its image is 8 squares from the bottom.2 + 8 = 10
- Halve it. The mirror line is halfway between them.10 ÷ 2 = 5
- Write the answer. 5 squares
Check. The point is 3 squares below the line (5 − 2), and the image is 3 squares above it. ✓
Watch out. Halve the total distance, not the distance from one edge only.
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.
Method. Think about where the image of a horizontal reflection goes.
- Look at the mirror line. A horizontal mirror line flips a shape up and down.up and down
- Look at the image. The image is above or below the shape, and it is not to the right.above or below
- Decide. So Sam is not right. A horizontal mirror line does not move the image to the right.No
Check. Only a vertical mirror line puts the image to the side. ✓
Watch out. Think about the direction of the mirror line first.
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.
Method. The point and its image are the same distance from the line on opposite sides.
- Find the distance from the point to the line. The point is 3 squares from the line.3 squares
- Find the distance from the image to the line. The image is also 3 squares from the line, on the other side.3 squares
- Add the two distances. The gap between the point and its image is both distances added together.3 + 3 = 6
- Write the answer. 6 squares apart
Check. The point and its image are 6 squares apart. ✓
Watch out. Add the two distances, one each side of the line.
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.
Method. The image is the same distance on the other side, so the point is the same distance on the other side too.
- Find the distance of the image. The image is 6 squares to the right of the mirror line.6 squares
- Find the distance of the point. The point is the same distance from the line, on the other side.6 squares
- Write the answer. 6 squares
Check. The point and its image are both 6 squares from the line. ✓
Watch out. The point is on the other side of the line from its 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.
Method. Count the distance to the mirror line, then count the same distance on the other side.
- Find the mirror line. The mirror line is 6 squares from the left edge.mirror line at 6
- Count the squares from the point to the line. The point is 4 squares from the line.4 squares
- Count the same number on the other side. The image is the same distance from the line, on the other side.6 + 4 = 10
- Write the answer. 10 squares from the left edge
Check. The point and its image are both 4 squares from the line. ✓
Watch out. Count from the left edge every time, so you do not mix up the two sides.
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.
Method. Count from each corner to the line, and then from the line to each image.
- Count from A to the line. A is at the right-hand corner of the blue triangle, 3 squares from the left edge.6 − 3 = 3
- Count from A' to the line. A' is 9 squares from the left edge, so it is 3 squares to the right of the line.9 − 6 = 3
- Decide. Both are the same distance from the line.Yes
Check. Each is 3 squares from the dashed line. ✓
Watch out. Count from the same line each time.
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.
Method. Count the squares from the point to the mirror line, then count the same number on the other side.
- Find the mirror line. The dashed red line is the mirror line.the dashed red line
- Count the squares from the point to the line. The point is 4 squares above the line.4 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.4 squares below the line
- Write the answer. 4 squares below the mirror line
Check. The point and its image are both 4 squares from the line. ✓
Watch out. The image is on the other side of the line, not on the same side.
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.
Method. Look at the two sides of the mirror line.
- Look at the left side of the line. The rectangle is the same on each side of the line.the same on each side
- Look at the corners. Each corner lands on a matching corner in the same place.matching corners
- Explain. A shape whose two halves match across the line is symmetrical about it, so its image lands on itself.The rectangle is symmetrical about the line
Check. A rectangle with the line through its middle is symmetrical. ✓
Watch out. A shape that lands on itself must match itself across the line.