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 = 5, 0

Answer 1

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

Given the original coordinates:

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

We can calculate the dilated coordinates \( F' \), \( G' \), and \( H' \) as follows:

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

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

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

So the coordinates of the vertices after the dilation are:

- \( F' = (-1, -2) \)
- \( G' = (0, -2) \)
- \( H' = (1, 0) \)