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