Question

Write the coordinates of the vertices after a dilation with a scale factor of
1
5
,
centered at the origin.
B
'
,
C
'
,
D
'
,
E
'
,
B = -10,-10
C = -10, 5
D = 10, 3
E = 10, 0

Answer 1

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

Let's find the new coordinates for each vertex:

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

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

3. For vertex \(D = (10, 3)\):
\[
D' = \left(10 \cdot \frac{1}{5}, 3 \cdot \frac{1}{5}\right) = \left(2, 0.6\right)
\]

4. For vertex \(E = (10, 0)\):
\[
E' = \left(10 \cdot \frac{1}{5}, 0 \cdot \frac{1}{5}\right) = \left(2, 0\right)
\]

The coordinates of the vertices after the dilation are:
- \(B' = (-2, -2)\)
- \(C' = (-2, 1)\)
- \(D' = (2, 0.6)\)
- \(E' = (2, 0)\)