Step by step
The question
Question: rotate the shape A(−2, −1), B(−4, −1) and C(−4, −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 A: go left 2
then down 1.
Now turn a half turn about O.
Everything turns with it.
Left 2 turns into right 2.
Down 1 turns into up 1.
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(−2, −1) goes to A'(2, 1).
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, −1): both signs change, so B' is (4, 1).
C is (−4, −3): both signs change, so C' is (4, 3).
Join the new points.
This new shape is called the image.
So the image is A'(2, 1), B'(4, 1) and C'(4, 3).
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.