Step by step
The question
Question: rotate the shape A(2, −1), B(4, −1) and C(2, −3) 90° counterclockwise about the origin.
1 Draw the shape
Put the points on the grid and join them.
2 Turn one point
Counterclockwise means the other way from the hands of a clock.
Start at the center O.
To reach A: go right 2
then down 1.
Now turn a quarter turn counterclockwise about O.
Everything turns with it.
Right 2 turns into up 2.
Down 1 turns into right 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'(1, 2).
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 first number gets a minus sign.
So the rule is: (x, y) goes to (−y, x).
4 Turn the other points
B is (4, −1): swap and change the sign of the first: B' is (1, 4).
C is (2, −3): swap and change the sign of the first: C' is (3, 2).
Join the new points.
This new shape is called the image.
So the image is A'(1, 2), B'(1, 4) and C'(3, 2).
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 counterclockwise.
Right!
Let's look back.
First: draw the shape.
Then: turn one point.
Then: find the rule.
Then: turn the other points.
Last: check.