Year 5: Flipping shapes: reflections
Part of the Year 5 reflection and translation chapter. Chapter overview · whole chapter on one page
Flipping shapes: reflections
A reflection flips a shape over a mirror line. The mirror line is shown as a dashed red line. Every point of the image is the same distance from the mirror line as the point it came from, but on the other side.
The image is the same size and the same shape as the original. It faces the other way round, like your reflection in a mirror. A mirror line can be vertical (up and down) or horizontal (across).
Key ideas
- A reflection flips a shape over a mirror line.
- The image is the same distance from the mirror line as the original, on the other side.
- The image is the same size and shape, but it faces the other way round.
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 2 squares left the line.2 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.2 squares right the line
- Write the answer. 2 squares to the right of the mirror line
Check. The point and its image are both 2 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. 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 below 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 above the line
- Write the answer. 5 squares above 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. 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 3 squares left the line.3 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.3 squares right the line
- Write the answer. 3 squares to the right of the mirror line
Check. The point and its image are both 3 squares from the line. ✓
Watch out. The image is on the other side of the line, not on the same side.
Watch out
A common mistake is to put the image on the same side of the mirror line as the original. The image must be on the other side. Also, a reflection is not a slide: the image is the same distance from the line on the other side, so count from the line, not from the original shape.
Exercise 10C Mirror lines and distances
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 corner A to the dashed mirror line.
- Find the mirror line. The dashed red line is the mirror line, at 6 squares from the left edge.line at 6
- Find corner A. Corner A is 4 squares from the left edge.A at 4
- Count the squares between them. The distance is the mirror position minus the position of A.6 − 4 = 2
- Write the answer. 2 squares
Check. The image A is on the other side, and it is also 2 squares from the line. ✓
Watch out. Count the squares between the corner and the line, not the squares of the whole house.
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 bottom of the triangle to the horizontal mirror line.
- Find the mirror line. The dashed red line is 5 squares above the bottom of the grid.line at 5
- Find the bottom of the triangle. The bottom of the triangle is on the bottom of the grid.bottom at 0
- Count the squares between them. Subtract the bottom from the line.5 − 0 = 5
- Write the answer. 5 squares
Check. The image of the bottom is 5 squares on the other side of the line. ✓
Watch out. The mirror line is horizontal, so count up and down, not across.
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 2 squares left the line.2 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.2 squares right the line
- Write the answer. 2 squares to the right of the mirror line
Check. The point and its image are both 2 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. 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 2 squares right the line.2 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.2 squares left the line
- Write the answer. 2 squares to the left of the mirror line
Check. The point and its image are both 2 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. 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 3 squares above the line.3 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.3 squares below the line
- Write the answer. 3 squares below the mirror line
Check. The point and its image are both 3 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 in the middle, so the image is the same distance on the other side.
- Find the mirror line. The mirror line is 4 squares from the left edge.line at 4
- Find the image. The image is 7 squares from the left edge.image at 7
- Count the distance from the line to the image. The point is the same distance on the other side of the line.7 − 4 = 3
- Write the answer. The point is 1 square from the left edge, which is 3 squares from the line.3 squares
Check. The point is at 1, and 4 − 1 = 3. ✓
Watch out. Count the distance from the line, not from the left edge.
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 B to the mirror line, then the same number on the other side.
- Find B. Corner B is 1 square from the left edge, at the top of the L.B at 1
- Count the squares from B to the line. The mirror line is 5 squares from the left edge.5 − 1 = 4
- Count the same number on the other side. The image of B is 4 squares on the other side of the line.5 + 4 = 9
- Write the answer. 4 squares
Check. B is 4 squares from the line, and so is B'. ✓
Watch out. B and its image are the same distance from 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. Think about what a reflection does to the distance.
- Check the distance of the point. The point is 3 squares from the line.3 squares
- Check the distance of the image. The image must be the same distance on the other side.3 squares
- Decide. Ali is not right, because the image is also 3 squares from the line.No
Check. A reflection keeps the same distance from the line. ✓
Watch out. Both the point and its image are the same distance from 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. Count the squares from the point to the line.
- Find the mirror line. The mirror line is 5 squares from the left edge.line at 5
- Find the point. The point is 2 squares from the left edge.point at 2
- Count the squares between them. Subtract the smaller position from the larger one.5 − 2 = 3
- Write the answer. 3 squares
Check. The image is also 3 squares from the line. ✓
Watch out. Count to the line, not all the way to the edge.
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 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 6 squares above the line.6 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.6 squares below the line
- Write the answer. 6 squares below the mirror line
Check. The point and its image are both 6 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. 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.
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 1 square left the line.1 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.1 squares right the line
- Write the answer. 1 square to the right of the mirror line
Check. The point and its image are both 1 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. 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 3 squares right the line.3 squares
- Count the same number on the other side. A reflection puts the image the same distance from the line, on the other side.3 squares left the line
- Write the answer. 3 squares to the left of the mirror line
Check. The point and its image are both 3 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. Reflect the shape once, then reflect the image again in the same line.
- First reflection. The shape moves to the other side of the line.the other side
- Second reflection. The image is reflected back across the same line, to the other side again.back to the first side
- Write the answer. Two flips in the same mirror line put the shape back where it started.back where it started
Check. Two reflections in the same line make the original again. ✓
Watch out. Two flips cancel each other out, like two equal moves.
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. A point on the mirror line is 0 squares away from the line.
- Count the distance. The point is on the line, so it is 0 squares from the line.0 squares
- Count the same distance on the other side. The image is 0 squares away on the other side, so it is on the same point.0 squares
- Write the answer. On the same point
Check. A point that is on the line does not move. ✓
Watch out. A point on the mirror line does not move at all.
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 a point and its image.
- Add the two distances from the edge. The point is 2 squares from the edge and the 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. 5 squares from the left edge
Check. The point is 3 squares from the line (5 − 2), and its image is 3 squares on the other side. ✓
Watch out. The mirror line is always halfway between a point and its image.