Step by step
The question
Question: rotate the shape A(1, 2) and B(4, 2) 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 A: go right 1
then up 2.
Now turn a half turn about O.
Everything turns with it.
Right 1 turns into left 1.
Up 2 turns into down 2.
We land on the new point A'.
We call the new point A prime.
The little mark means: the new A.
3 Find the rule
Look at the numbers of A and A'.
A(1, 2) goes to A'(−1, −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
B is (4, 2): both signs change, so B' is (−4, −2).
Join the new points.
This new shape is called the image.
So the image is A'(−1, −2) and B'(−4, −2).
5 Check
Let's check B on the grid.
Join O to B
and O to B'.
B, O and B' 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.