Question

Write the coordinates of the vertices after a dilation with a scale factor of
1
5
,
centered at the origin.
F
'
,
G
'
,
H
'
,


F = -5, -10
g = 0, -10
H = 3, 0

Answer 1

To perform a dilation centered at the origin with a scale factor of \(\frac{1}{5}\), you'll multiply each coordinate of the vertices by the scale factor.

The original coordinates are:

- \( F(-5, -10) \)
- \( G(0, -10) \)
- \( H(3, 0) \)

Now, we apply the scale factor of \(\frac{1}{5}\):

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

2. For point \( G \):
\[
G' = \left(0 \cdot \frac{1}{5}, -10 \cdot \frac{1}{5}\right) = \left(0, -2\right)
\]

3. For point \( H \):
\[
H' = \left(3 \cdot \frac{1}{5}, 0 \cdot \frac{1}{5}\right) = \left(\frac{3}{5}, 0\right)
\]

Thus, the coordinates of the vertices after the dilation are:

- \( F'(-1, -2) \)
- \( G'(0, -2) \)
- \( H'\left(\frac{3}{5}, 0\right) \)