Describe the transformation A(2, 1) B(3, 1) C(2, 3) to A'(-2, -1)…

Step by step

The question

Question: describe the move that takes A(2, 1), B(3, 1) and C(2, 3) to A'(−2, −1), B'(−3, −1) and C'(−2, −3).

1 Draw both shapes

Put the shape on the grid

and its image.

2 Compare A and A'

Look at what happened to the numbers of A: A(2, 1) went to A'(−2, −1).

x went from 2 to −2.

y went from 1 to −1.

Both signs changed.

3 Name the move

So the rule is: (x, y) goes to (−x, −y).

Careful!

Both signs changed.

A flip in an axis changes only one sign.

Both is a half turn.

That is the rule of a turn about O.

So the move is a rotation of 180° about the origin.

4 Check

Let's check the rule on the other points.

B goes to (−3, −1).

That is B'.

C goes to (−2, −3): C'.

Right!

Let's look back.

First: draw both shapes.

Then: compare A and A'.

Then: name the move.

Last: check.