Step by step
The question
Question: dilate the point P(6, −4) by scale factor ½.
P = (6, −4)
= scale factor 12
1 Draw the shape
Put the point on the grid.
2 Multiply each point
Scale factor one half makes the shape half as big.
Every number is multiplied by one half.
scale factor ½ → half as big
We call the new point P prime.
The little mark means: the new P.
P is (6, −4).
Half of 6 is 3.
Half of −4 is −2.
So P' is (3, −2).
P(6, −4) → (12 × 6, 12 × −4) = P'(3, −2)
Careful!
Half as big means divide every number by 2.
Taking 2 away would slide the shape.
Careful: not P'(6 − 2, −4 − 2) ✗
3 The new point
So the image is P'(3, −2).
P' = (3, −2)
4 Check
Let's check P.
Draw a line from O through P' to P.
From O to P: right 6, down 4.
O → P: right 6, down 4
From O to P': right 3, down 2.
That is half the moves to P.
So P' is on the same line from O, half as far.
Right!
O → P': right 3, down 2
Let's look back.
First: draw the shape.
Then: multiply each point.
Then: the new point.
Last: check.
Answer
P' = (3, −2)