Asked by liquidlew

































Write the coordinates of the vertices after a dilation with a scale factor of
1
4
,
centered at the origin.
R
'
,
S
'
,
T
'
,

R=-8,-8
S = -8,8
T = 0, -8

Answers

Answered by GPT-4o mini
To perform a dilation with a scale factor of \( \frac{1}{4} \) centered at the origin, you multiply each coordinate of the vertices by the scale factor.

Given the vertices:
- \( R = (-8, -8) \)
- \( S = (-8, 8) \)
- \( T = (0, -8) \)

Now, apply the scale factor of \( \frac{1}{4} \) to each vertex:

1. For vertex \( R' \):
\[
R' = \left(-8 \cdot \frac{1}{4}, -8 \cdot \frac{1}{4}\right) = \left(-2, -2\right)
\]

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

3. For vertex \( T' \):
\[
T' = \left(0 \cdot \frac{1}{4}, -8 \cdot \frac{1}{4}\right) = \left(0, -2\right)
\]

Thus, the coordinates of the vertices after the dilation are:
- \( R' = (-2, -2) \)
- \( S' = (-2, 2) \)
- \( T' = (0, -2) \)
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