Step by step
The question
Question: rotate the point P(4, 1) 90° counterclockwise about the origin.
1 Draw the shape
Put the point on the grid.
2 Turn one point
Counterclockwise means the other way from the hands of a clock.
Start at the center O.
To reach P: go right 4
then up 1.
Now turn a quarter turn counterclockwise about O.
Everything turns with it.
Right 4 turns into up 4.
Up 1 turns into left 1.
We land on the new point P'.
We call the new point P prime.
The little mark means: the new P.
3 Find the rule
Look at the numbers of P and P'.
P(4, 1) goes to P'(−1, 4).
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).
So the image is P'(−1, 4).
4 Check
Let's check P on the grid.
Join O to P
and O to P'.
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.
Last: check.