Step by step
The question
Question: dilate the point P(2, 3) by scale factor 3.
1 Draw the shape
Put the point on the grid.
2 Multiply each point
Scale factor 3 makes every length 3 times as long.
From O, each point goes 3 times as far, in the same direction.
So its move across and its move up are both 3 times as big.
That is why we multiply both numbers by 3.
We call the new point P prime.
The little mark means: the new P.
P is (2, 3).
3 times 2 is 6.
3 times 3 is 9.
So P' is (6, 9).
Careful!
A dilation multiplies.
Adding 3 would slide the shape, not make it bigger.
3 The new point
So the image, the new point, is P'(6, 9).
4 Check
Let's check P.
Draw a line from O through P to P'.
From O to P: right 2, up 3.
From O to P': right 6, up 9.
That is 3 times the moves to P.
So P' is on the same line from O, 3 times as far.
Right!
Let's look back.
First: draw the shape.
Then: multiply each point.
Then: the new point.
Last: check.