Question

Write the coordinates of the vertices after a dilation with a scale factor of
1
2
,
centered at the origin.
A
'
,
B
'
,
C
'
,
D
'
,

a = -6, -8
b = -6, -2
c = -2, 8
d = -2, -8

Answer 1

To find the coordinates of the vertices after a dilation with a scale factor of \( \frac{1}{2} \) centered at the origin, you multiply each coordinate by the scale factor.

The original coordinates are:
- A = (-6, -8)
- B = (-6, -2)
- C = (-2, 8)
- D = (-2, -8)

Now we will apply the scale factor of \( \frac{1}{2} \):

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

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

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

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

Now we can list the coordinates of the vertices after the dilation:
- A' = (-3, -4)
- B' = (-3, -1)
- C' = (-1, 4)
- D' = (-1, -4)

So the final coordinates are:
- A' = (-3, -4)
- B' = (-3, -1)
- C' = (-1, 4)
- D' = (-1, -4)