Step by step
The question
Question: rotate the shape A(−1, 2), B(−3, 2) and C(−3, 4) 90° clockwise about the origin.
1 Draw the shape
Put the points on the grid and join them.
2 Turn one point
Clockwise means the way the hands of a clock turn.
Start at the center O.
To reach A: go left 1
then up 2.
Now turn a quarter turn clockwise about O.
Everything turns with it.
Left 1 turns into up 1.
Up 2 turns into right 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'(2, 1).
Careful!
A quarter turn swaps the two numbers.
Changing a sign alone is a flip, not a turn.
The two numbers swap places, and the new second number gets a minus sign.
So the rule is: (x, y) goes to (y, −x).
4 Turn the other points
B is (−3, 2): swap and change the sign of the second: B' is (2, 3).
C is (−3, 4): swap and change the sign of the second: C' is (4, 3).
Join the new points.
This new shape is called the image.
So the image is A'(2, 1), B'(2, 3) and C'(4, 3).
5 Check
Let's check B on the grid.
Join O to B
and O to B'.
They make a right angle: a quarter turn.
And it turns clockwise.
Right!
Let's look back.
First: draw the shape.
Then: turn one point.
Then: find the rule.
Then: turn the other points.
Last: check.