Coordinates and trigonometry · Ages 12–13

Reflection worksheet

Part of: First steps in coordinates

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Coordinates and trigonometry · Ages 12–13

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Reflected in the y-axis, (6, −3) goes to (, ).
Fill in each blank
Answer:
2.Reflected in the x-axis, (3, −1) goes to (, ).
Fill in each blank
Answer:
3.Reflected in the y-axis, (3, −4) goes to (, ).
Fill in each blank
Answer:
4.Reflected in the x-axis, P goes to (−6, −7). P's y-coordinate is .
Answer:
5.Reflected in the x-axis, P goes to (−8, −9). P's y-coordinate is .
Answer:
6.Reflected in the line x = 2, A(6, 6) goes to (, ).
Fill in each blank
Answer:
7.Reflected in the line y = 1, (6, 6) goes to (, ).
Fill in each blank
Answer:
8.Reflected in the line y = 4, (−5, 5) goes to (, ).
Fill in each blank
Answer:
9.Reflected in the line x = −2, A(−4, 5) goes to (, ).
Fill in each blank
Answer:

10.What is the image of (−2, 1) reflected in the y-axis?
- A. (2, 1)
- B. (−2, −1)
- C. (2, −1)
- D. (1, −2)
Choose the right answer
Answer:
11.Triangle ABC is reflected in the y-axis to A′B′C′. Which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:
12.(9, −8) and (−9, 8) are reflections of each other in the x-axis.
True or false?
Answer:

13.A(−2, −3) is reflected in the x-axis to B, and B translated 1 unit right to C. B is (, ) and C is (, ).
Fill in each blank
Working:
Answer:
14.A mirror stands along the y-axis. A pen's tip is at (−5, −6); its image in the mirror is at (, ).
Fill in each blank
Working:
Answer:
15.Reflected in the y-axis, P(4k − 8, 4) goes to (−8, 4). What is k?
Working:
Answer:
16.A(4, −1) is reflected in the x-axis to B, and B in the y-axis to C. What are C's coordinates?
- A. (−1, 4)
- B. (4, 1)
- C. (−4, −1)
- D. (−4, 1)
Choose the right answer
Working:
Answer:
17.A(6, −2) reflected in the x-axis is B, and in the y-axis C. What is the area of triangle ABC, in square units?
Working:
Answer:
18.Triangle ABC is reflected in the y-axis to A′B′C′. With A(5, −1) and B(2, 5), A′ is (, ) and B′ is (, ).
Fill in each blank
Working:
Answer:

Show the answers and working

Reflection worksheet: Answers and working

1. −6, −3
In the y-axis: y stays and x changes sign, giving (−6, −3). Both are 6 from the y-axis.
2. 3, 1
In the x-axis: x stays and y changes sign, giving (3, 1). The point and its image are both 1 from the x-axis.
3. −3, −4
In the y-axis: y stays and x changes sign, giving (−3, −4). Both are 3 from the y-axis.
4. 7
Reflect the image in the x-axis again and it comes back to P: P is (−6, 7).
5. 9
Reflect the image in the x-axis again and it comes back to P: P is (−8, 9).
6. −2, 6
A is 4 units from the line x = 2, and its image as far the other side: x = 2 − 4 = −2. The mirror is vertical, so y stays.
7. 6, −4
y = 1 is horizontal, so x stays; the point is 5 units from it and the image as far the other side: y = 1 − 5 = −4.
8. −5, 3
y = 4 is horizontal, so x stays; the point is 1 unit from it and the image as far the other side: y = 4 − 1 = 3.
9. 0, 5
A is 2 units from the line x = −2, and its image as far the other side: x = −2 + 2 = 0. The mirror is vertical, so y stays.

10. A. (2, 1)
In the y-axis the point keeps its distance from the y-axis on the other side: x changes sign, y stays, (2, 1).
11. B
In the y-axis every corner's x changes sign and y stays: the image sits the other side of the y-axis, left and right swapped.
12. False
In the x-axis, x stays and y changes sign: the image of (9, −8) is (9, 8).

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. −2, 3, −1, 3
In the x-axis: B(−2, 3); 1 right adds 1 to x: C(−1, 3).
14. 5, −6
A mirror along the y-axis reflects in the y-axis: y stays and x changes sign, giving (5, −6).
15. 4
In the y-axis x changes sign, so P's x is 8: 4k − 8 = 8, k = 4.
16. D. (−4, 1)
In the x-axis: B(4, 1); then in the y-axis: C(−4, 1). Both signs have changed.
17. 24
AB is vertical, 2 × 2 = 4 long; AC is horizontal, 2 × 6 = 12; the right angle is at A, so the area is 12 × 4 × 12 = 24.
18. −5, −1, −2, 5
In the y-axis every corner's x changes sign and y stays: A′(−5, −1), B′(−2, 5).

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