Step by step
The question
Question: reflect the shape A(1, 3), B(2, 5) and C(4, 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: right 1, down 1.
Then go the same again, past the line.
We call the new point A prime.
The little mark means: the new A.
A is (1, 3).
Across the mirror line, A' is (3, 1).
Careful!
Over the line y = x, the two numbers swap places.
Their signs do not change.
B is (2, 5).
Across the mirror line, B' is (5, 2).
C is (4, 3).
Across the mirror line, C' is (3, 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, 2) and C'(3, 4).
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.