Step by step
The question
Question: reflect the shape A(1, 2), B(3, 2) and C(3, 4) in the line y = x, then reflect it in the y-axis.
1 Draw the shape
Put the points on the grid and join them.
2 First: reflect in the line y = x
Reflection in the line y = x: x and y swap places.
The rule is: (x, y) goes to (y, x).
A(1, 2) goes to A'(2, 1).
B(3, 2) goes to B'(2, 3).
C(3, 4) goes to C'(4, 3).
Join them.
This is the first image.
3 Then: reflect in the y-axis
Reflection in the y-axis: x changes sign, y stays the same.
The rule is: (x, y) goes to (−x, y).
A'(2, 1) goes to A''(−2, 1).
Careful!
The second move starts from the new points A', B' and C'.
Not from the first shape.
B'(2, 3) goes to B''(−2, 3).
C'(4, 3) goes to C''(−4, 3).
Join them.
This is the final image.
So the final image is A''(−2, 1), B''(−2, 3) and C''(−4, 3).
4 Check
Let's check in one go.
Put the first rule's answer (y, x) into the second rule.
We get (−y, x).
A goes straight to (−2, 1).
That is A''.
Right!
Let's look back.
First: draw the shape.
Then: reflect in the line y = x.
Then: reflect in the y-axis.
Last: check.