Step by step
The question
Question: rotate the shape A(1, 1), B(3, 1), C(3, 2) and D(1, 2) 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 B: go right 3
then up 1.
Now turn a quarter turn counterclockwise about O.
Everything turns with it.
Right 3 turns into up 3.
Up 1 turns into left 1.
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(3, 1) goes to B'(−1, 3).
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
A is (1, 1): swap and change the sign of the first: A' is (−1, 1).
C is (3, 2): swap and change the sign of the first: C' is (−2, 3).
D is (1, 2): swap and change the sign of the first: D' is (−2, 1).
Join the new points.
This new shape is called the image.
So the image is A'(−1, 1), B'(−1, 3), C'(−2, 3) and D'(−2, 1).
5 Check
Let's check A on the grid.
Join O to A
and O to A'.
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.