Question

Write the coordinates of the vertices after a dilation with a scale factor of
1
3
,
centered at the origin.
D
'
,
E
'
,
F
'
,
G
'
,


D= -6, -9
E = 3, -9
F = 3, -3
G = -6, -3

Answer 1

To find the coordinates of the vertices after a dilation with a scale factor of \(\frac{1}{3}\) centered at the origin, you multiply each coordinate of the points by the scale factor.

Given the points:
- \(D (-6, -9)\)
- \(E (3, -9)\)
- \(F (3, -3)\)
- \(G (-6, -3)\)

We can apply the dilation:

1. For point \(D\):
\[
D' = \left(-6 \times \frac{1}{3}, -9 \times \frac{1}{3}\right) = \left(-2, -3\right)
\]

2. For point \(E\):
\[
E' = \left(3 \times \frac{1}{3}, -9 \times \frac{1}{3}\right) = \left(1, -3\right)
\]

3. For point \(F\):
\[
F' = \left(3 \times \frac{1}{3}, -3 \times \frac{1}{3}\right) = \left(1, -1\right)
\]

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

Therefore, the coordinates of the vertices after dilation are:
- \(D' = (-2, -3)\)
- \(E' = (1, -3)\)
- \(F' = (1, -1)\)
- \(G' = (-2, -1)\)