Step by step
The question
Question: rotate the point P(5, −2) 270° clockwise about the origin.
1 Draw the shape
Put the point on the grid.
2 Turn one point
Clockwise means the way the hands of a clock turn.
Three quarter turns clockwise end in the same place as one quarter turn counterclockwise.
Start at the center O.
To reach P: go right 5
then down 2.
Now turn three quarter turns clockwise about O.
Everything turns with it.
Right 5 turns into up 5.
Down 2 turns into right 2.
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(5, −2) goes to P'(2, 5).
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'(2, 5).
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.