Step by step
The question
Question: dilate the point P(2, 3) by scale factor 2.
P = (2, 3)
= scale factor 2
1 Draw the shape
Put the point on the grid.
2 Multiply each point
Scale factor 2 makes the shape 2 times as big.
Every number is multiplied by 2.
scale factor 2 → 2 times as big
We call the new point P prime.
The little mark means: the new P.
P is (2, 3).
2 times 2 is 4.
2 times 3 is 6.
So P' is (4, 6).
P(2, 3) → (2 × 2, 2 × 3) = P'(4, 6)
Careful!
A dilation multiplies.
Adding 2 would slide the shape, not make it bigger.
Careful: not P'(2 + 2, 3 + 2) ✗
3 The new point
So the image is P'(4, 6).
P' = (4, 6)
4 Check
Let's check P.
Draw a line from O through P to P'.
From O to P: right 2, up 3.
O → P: right 2, up 3
From O to P': right 4, up 6.
That is 2 times the moves to P.
So P' is on the same line from O, 2 times as far.
Right!
O → P': right 4, up 6
Let's look back.
First: draw the shape.
Then: multiply each point.
Then: the new point.
Last: check.
Answer
P' = (4, 6)