Step by step
The question
Question: dilate the point P(4, −2) by scale factor 2.
1 Draw the shape
Put the point on the grid.
2 Multiply each point
Scale factor 2 makes every length 2 times as long.
From O, each point goes 2 times as far, in the same direction.
So its move across and its move up are both 2 times as big.
That is why we multiply both numbers by 2.
We call the new point P prime.
The little mark means: the new P.
P is (4, −2).
2 times 4 is 8.
2 times −2 is −4.
So P' is (8, −4).
Careful!
A dilation multiplies.
Adding 2 would slide the shape, not make it bigger.
3 The new point
So the image, the new point, is P'(8, −4).
4 Check
Let's check P.
Draw a line from O through P to P'.
From O to P: right 4, down 2.
From O to P': right 8, down 4.
That is 2 times the moves to P.
So P' is on the same line from O, 2 times as far.
Right!
Let's look back.
First: draw the shape.
Then: multiply each point.
Then: the new point.
Last: check.