Reflected in the x-axis, P goes to (−2, 4). P's y-coordinate is □.

−4. Reflect the image in the x-axis again and it comes back to P: P is (−2, −4).

(−7, 9) and (−7, −9) are reflections of each other in the x-axis. True or false?

True. In the x-axis, x stays and y changes sign: the image of (−7, 9) is (−7, −9).

Reflected in the line y = 1, (3, −1) goes to (□, □). Fill in each blank

3, 3. y = 1 is horizontal, so x stays; the point is 2 units from it and the image as far the other side: y = 1 + 2 = 3.

First steps in coordinates · Ages 12–13

Reflection

In the x-axis x stays; in the y-axis y stays.

How to do it

Method

In the x-axis x stays; in the y-axis y stays

(3, −2): in the x-axis (3, 2), in the y-axis (−3, −2)

Another way

Count to the mirror

(1, 2) in x = 3: 2 to the line, 2 beyond, (5, 2)

In full

Reflected in the x-axis, (x, y) goes to (x, −y): x stays and y changes sign, so the point and its image are either side of the x-axis, equally far from it. Reflected in the y-axis, it goes to (−x, y): y stays and x changes sign. To remember: the coordinate named by the mirror axis stays. (3, −2) reflected in the x-axis is (3, 2), and in the y-axis (−3, −2). With a mirror line x = a or y = b, count squares: the image is as far beyond the line as the point is before it, so (1, 2) in x = 3 goes to (5, 2); or work it out as x′ = 2a − x.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
Reflected in the x-axis, P goes to (−2, 4). P's y-coordinate is .
Show the answer and working
Answer: −4
Reflect the image in the x-axis again and it comes back to P: P is (−2, −4).
Example 2
(−7, 9) and (−7, −9) are reflections of each other in the x-axis.
True or false?
Show the answer and working
Answer: True
In the x-axis, x stays and y changes sign: the image of (−7, 9) is (−7, −9).
Example 3
Reflected in the line y = 1, (3, −1) goes to (, ).
Fill in each blank
Show the answer and working
Answer: 3, 3
y = 1 is horizontal, so x stays; the point is 2 units from it and the image as far the other side: y = 1 + 2 = 3.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Reflected in the x-axis, (−4, 7) goes to (, ).
Fill in each blank
Answer:
2.(9, 9) and (9, 9) are reflections of each other in the x-axis.
True or false?
Answer:
3.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:
4.Reflected in the x-axis, P goes to (−7, 5). P's y-coordinate is .
Answer:
5.Reflected in the line x = 2, A(3, −1) goes to (, ).
Fill in each blank
Answer:

All the answers

1. −4, −7
2. False
3. B
4. −5
5. 1, −1

Free worksheet: ReflectionWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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