Shape and space · Ages 9–10
Reflections worksheet
Part of: Coordinates and moving shapes
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Reflections worksheet
Shape and space · Ages 9–10
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The green line is a mirror line. Point A reflects to A′ at (, ).
Fill in each blank
Answer:
2.Triangle ABC is reflected in its side AC (the green mirror line). How many squares apart are B and its image B′?
Answer:
3.The mirror line runs straight across through (0, 2). The point (5, 0) reflects to (, ).
Fill in each blank
Answer:
4.The mirror line runs straight across through (0, 8). The point (7, 9) reflects to (, ).
Fill in each blank
Answer:
5.The mirror line runs straight across through (0, 6). The point (7, 8) reflects to (, ).
Fill in each blank
Answer:
6.The mirror line slants through (0, 0), (1, 1), (2, 2), …. The point (4, 3) reflects to (, ).
Fill in each blank
Answer:
7.The mirror line slants through (0, 0), (1, 1), (2, 2), …. The point (8, 2) reflects to (, ).
Fill in each blank
Answer:
8.The mirror line slants through (0, 0), (1, 1), (2, 2), …. The point (6, 4) reflects to (, ).
Fill in each blank
Answer:
9.The mirror line slants through (0, 0), (1, 1), (2, 2), …. The point (6, 10) reflects to (, ).
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
10.Which picture shows the reflection (blue) of the orange triangle in the green mirror line correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
11.The green line is a mirror line. Shape Q is the reflection of shape P.
True or false?
Answer:
12.The green slanting line is the mirror line, through (0, 0), (1, 1), (2, 2), …. Which picture shows the orange triangle's image (blue) correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
Part C: Word problems (4 marks each)
13.On a grid picture of Victoria Harbour, the water is a line across through (0, 4), like a mirror. A tower's top is at (4, 8); the top of its reflection in the water is at (, ).
Fill in each blank
Working:
Answer:
14.Ka-lok stands a rectangular tile, 5 cm long and 2 cm wide, with one long side against a mirror. The tile and its reflection together look like one big rectangle. What is its area in cm²?
Working:
Answer:
15.May stands 4 steps in front of a tall mirror. How many steps apart are May and May's reflection?
Working:
Answer:
16.Ming folds squared paper along the upright line through (5, 0) and pokes a hole through at (6, 3). Unfolded, the other hole is at (, ).
Fill in each blank
Working:
Answer:
17.On a grid picture of Victoria Harbour, the water is a line across through (0, 2), like a mirror. A tower's top is at (5, 3); the top of its reflection in the water is at (, ).
Fill in each blank
Working:
Answer:
18.Tsz-ching stands 6 steps in front of a tall mirror. How many steps apart are Tsz-ching and Tsz-ching's reflection?
Working:
Answer:
Show the answers and working
Reflections worksheet: Answers and working
Part A: Working out and filling in
1. 1, 1
Count how many squares A is from the green mirror. The image is on the other side, at the same height.
A is 2 squares from the mirror, so A′ is 2 on the other side, at the same height: (1, 1).
2. 6 squares
AC is on the mirror and stays put. First count how many squares B is to the right of it.
AC is on the mirror and stays put. B is 3 right of the mirror, so B′ is 3 to its left: 3 + 3 = 6 apart.
3. 5, 4
A mirror across only flips up and down, so x stays. First see how far 0 is from 2.
A mirror across keeps x; the point is 2 from the line, so its image is 2 on the other side: (5, 4).
4. 7, 7
A mirror across only flips up and down, so x stays. First see how far 9 is from 8.
A mirror across keeps x; the point is 1 from the line, so its image is 1 on the other side: (7, 7).
5. 7, 4
A mirror across only flips up and down, so x stays. First see how far 8 is from 6.
A mirror across keeps x; the point is 2 from the line, so its image is 2 on the other side: (7, 4).
6. 3, 4
Every point on this line has x equal to y. Think what reflecting does to the two numbers of (4, 3).
Measured along the squares' diagonals, the point and its image are the same distance from the line, and x and y swap: (3, 4).
7. 2, 8
Every point on this line has x equal to y. Think what reflecting does to the two numbers of (8, 2).
Measured along the squares' diagonals, the point and its image are the same distance from the line, and x and y swap: (2, 8).
8. 4, 6
Every point on this line has x equal to y. Think what reflecting does to the two numbers of (6, 4).
Measured along the squares' diagonals, the point and its image are the same distance from the line, and x and y swap: (4, 6).
9. 10, 6
Every point on this line has x equal to y. Think what reflecting does to the two numbers of (6, 10).
Measured along the squares' diagonals, the point and its image are the same distance from the line, and x and y swap: (10, 6).
Part B: Choose, or true or false
10. C
See how far the right angle is from the mirror: its image must be just as far on the other side, and the shape flipped.
Each corner flips to the other side of the mirror, the same distance from it and at the same height.
11. False
See how far P's right angle is from the mirror. Is Q's just as far on the other side, and is Q flipped?
The reflection has each corner of P flipped to the other side of the mirror, the same distance from it.
12. B
In this slanting mirror (x, y) goes to (y, x). Find where the right angle (5, 1) goes first.
In this slanting mirror the image of (x, y) is (y, x): the right angle (5, 1) goes to (1, 5).
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 4, 0
The water is a mirror across, so x stays. First count how far the top is above the water.
The top is 4 above the water, so its reflection is 4 below, straight under it: (4, 0).
14. 20 cm²
The reflection is the same size as the tile. How many tiles' worth make the big rectangle?
The reflection is the same size as the tile, so it is 2 tiles: 2 × 5 × 2 = 20 cm².
15. 8 steps
How far behind the mirror is the reflection? There are two distances between May and the reflection.
The reflection is as far behind the mirror, 4 steps: 4 + 4 = 8.
16. 4, 3
The fold is the mirror line, and the height stays. First count how far the hole is from the fold.
The fold is the mirror line: the hole is 1 from it, so the other is 1 on the other side at the same height: (4, 3).
17. 5, 1
The water is a mirror across, so x stays. First count how far the top is above the water.
The top is 1 above the water, so its reflection is 1 below, straight under it: (5, 1).
18. 12 steps
How far behind the mirror is the reflection? There are two distances between Tsz-ching and the reflection.
The reflection is as far behind the mirror, 6 steps: 6 + 6 = 12.
Numsprite · numsprite.com/en/worksheets/coordinates-and-transformations/reflections
Practise it in the gameReflections · Unlimited questions, no download