Step by step
The question
Question: reflect the shape A(−1, 1), B(1, 2) and C(0, 4) in the line x = 2.
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 = 2.
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: 3.
Then count 3 more on the other side.
We call the new point A prime.
The little mark means: the new A.
A is 3 left of the line.
Its image is 3 right of it.
Its y stays 1.
So A' is (5, 1).
Careful!
Count to the mirror line x = 2, not to the y-axis.
B is 1 left of it, so B' is 1 right of: (3, 2).
C is 2 left of it, so C' is 2 right of: (4, 4).
4 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(5, 1), B'(3, 2) and C'(4, 4).
5 Check
Let's check: the mirror line is halfway between a point and its image.
Halfway between −1 and 5: add them, then divide by 2.
That is 2: the line x = 2.
Right!
B: halfway between 1 and 3 is 2 too.
C: halfway between 0 and 4 is 2 too.
Let's look back.
First: draw the shape.
Then: draw the mirror line.
Then: reflect each point.
Then: draw the image.
Last: check.