Question

Write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.
P
'
,
Q
'
,
R
'
,


p = -3,-3
q = 2, -3
r = -2, -2

Answer 1

To perform a dilation centered at the origin with a scale factor of 2, you multiply each coordinate of the vertices by the scale factor.

Given the points:
- \( P(-3, -3) \)
- \( Q(2, -3) \)
- \( R(-2, -2) \)

Now, let's apply the dilation:

1. For point \( P' \):
\[
P' = (2 \times -3, 2 \times -3) = (-6, -6)
\]

2. For point \( Q' \):
\[
Q' = (2 \times 2, 2 \times -3) = (4, -6)
\]

3. For point \( R' \):
\[
R' = (2 \times -2, 2 \times -2) = (-4, -4)
\]

So, the coordinates of the vertices after the dilation are:
- \( P'(-6, -6) \)
- \( Q'(4, -6) \)
- \( R'(-4, -4) \)