Step by step
The question
Question: reflect the shape A(1, −1), B(3, −1) and C(3, −4) in the line x = −1.
1 Draw the shape
Put the points on the grid and join them.
2 Draw the mirror line
The mirror line is the line x = −1.
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: 2.
Then count 2 more on the other side.
We call the new point A prime.
The little mark means: the new A.
A is 2 right of the line.
Its image is 2 left of it.
Its y stays −1.
So A' is (−3, −1).
Careful!
Count to the mirror line x = −1, not to the y-axis.
B is 4 right of it, so B' is 4 left of: (−5, −1).
C is 4 right of it, so C' is 4 left of: (−5, −4).
4 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(−3, −1), B'(−5, −1) and C'(−5, −4).
5 Check
Let's check: the mirror line is halfway between a point and its image.
Halfway between 1 and −3: add them, then divide by 2.
That is −1: the line x = −1.
Right!
B: halfway between 3 and −5 is −1 too.
C: halfway between 3 and −5 is −1 too.
Let's look back.
First: draw the shape.
Then: draw the mirror line.
Then: reflect each point.
Then: draw the image.
Last: check.