Step by step
The question
Question: rotate the shape A(3, 0), B(4, 2) and C(2, 3) 180° about the origin.
1 Draw the shape
Put the points on the grid and join them.
2 Turn one point
Start at the center O.
To reach B: go right 4
then up 2.
Now turn a half turn about O.
Everything turns with it.
Right 4 turns into left 4.
Up 2 turns into down 2.
We land on the new point B'.
We call the new point B prime.
The little mark means: the new B.
3 Find the rule
Look at the numbers of B and B'.
B(4, 2) goes to B'(−4, −2).
Careful!
A half turn changes both signs.
Changing one sign is a flip, not a turn.
Both numbers stay in their places, and both change sign.
So the rule is: (x, y) goes to (−x, −y).
4 Turn the other points
A is (3, 0): both signs change, so A' is (−3, 0).
C is (2, 3): both signs change, so C' is (−2, −3).
Join the new points.
This new shape is called the image.
So the image is A'(−3, 0), B'(−4, −2) and C'(−2, −3).
5 Check
Let's check A on the grid.
Join O to A
and O to A'.
A, O and A' are on one straight line, with O in the middle.
That is a half turn.
Right!
Let's look back.
First: draw the shape.
Then: turn one point.
Then: find the rule.
Then: turn the other points.
Last: check.