Question

Write the coordinates of the vertices after a dilation with a scale factor of
1
2
,
centered at the origin.
P
'
,
Q
'
,
R
'
,
S
'
,


p = -10, -10
q = -10, 6
r = -8, 10
s = -8, -6

Answer 1

To perform a dilation centered at the origin with a scale factor of \( \frac{1}{2} \), we multiply each coordinate of the original points by the scale factor.

The original coordinates of the vertices are:
- \( P(-10, -10) \)
- \( Q(-10, 6) \)
- \( R(-8, 10) \)
- \( S(-8, -6) \)

Now, we will apply the dilation:

1. For \( P' \):
\[
P' = \left( -10 \times \frac{1}{2}, -10 \times \frac{1}{2} \right) = \left( -5, -5 \right)
\]

2. For \( Q' \):
\[
Q' = \left( -10 \times \frac{1}{2}, 6 \times \frac{1}{2} \right) = \left( -5, 3 \right)
\]

3. For \( R' \):
\[
R' = \left( -8 \times \frac{1}{2}, 10 \times \frac{1}{2} \right) = \left( -4, 5 \right)
\]

4. For \( S' \):
\[
S' = \left( -8 \times \frac{1}{2}, -6 \times \frac{1}{2} \right) = \left( -4, -3 \right)
\]

Thus, the coordinates of the dilated vertices are:
- \( P'(-5, -5) \)
- \( Q'(-5, 3) \)
- \( R'(-4, 5) \)
- \( S'(-4, -3) \)