Step by step
The question
Question: reflect the shape A(−3, 1), B(−1, 1) and C(−1, 4) in the x-axis.
1 Draw the shape
Put the points on the grid and join them.
2 Draw the mirror line
The mirror line is the x-axis.
Reflecting flips the shape over the line, like a mirror.
Each point lands just as far away, on the other side.
3 Reflect each point
From A, count straight to the mirror line: 1.
Then count 1 more on the other side.
We call the new point A prime.
The little mark means: the new A.
A is 1 above the x-axis.
Its image is 1 below it.
Its x stays −3.
So A' is (−3, −1).
Careful!
The x-axis is flat.
The flip goes up or down, so y changes.
x stays.
B is 1 above it, so B' is 1 below: (−1, −1).
C is 4 above it, so C' is 4 below: (−1, −4).
4 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(−3, −1), B'(−1, −1) and C'(−1, −4).
5 Check
Let's check with the rule for the x-axis: x stays the same, y changes sign.
It gives the same points.
Right!
Let's look back.
First: draw the shape.
Then: draw the mirror line.
Then: reflect each point.
Then: draw the image.
Last: check.