Step by step
The question
Question: reflect the shape A(−2, 1), B(−1, 4) and C(1, 3) in the line y = x.
1 Draw the shape
Put the points on the grid and join them.
2 Draw the mirror line
The mirror line is the line y = x.
It goes through (0, 0), (1, 1), (2, 2) and so on.
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, go straight to the mirror line, at a right angle to it.
Then go the same again, past the line.
We call the new point A prime.
The little mark means: the new A.
A is (−2, 1).
Across the mirror line, A' is (1, −2).
Careful!
Over the line y = x, the two numbers swap places.
Their signs do not change.
B is (−1, 4).
Across the mirror line, B' is (4, −1).
C is (1, 3).
Across the mirror line, C' is (3, 1).
4 Draw the image
Join the new points.
This new shape is called the image.
So the image is A'(1, −2), B'(4, −1) and C'(3, 1).
5 Check
Let's check with the rule for the line y = x: x and y swap places.
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.