Question

write the coordinates of the vertices after a dilation with a scale factor of (\frac{1}{4}), centered at the origin.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph:

• \( D(-4, 0) \)
• \( E(-4, 8) \)
• \( F(8, -4) \)
• \( G(8, -8) \)

Step2: Apply dilation formula

The rule for dilation centered at the origin with scale factor \( k \) is \( (x, y) \to (kx, ky) \). Here, \( k = \frac{1}{4} \).

For \( D(-4, 0) \):

Multiply each coordinate by \( \frac{1}{4} \):
\( x = -4 \times \frac{1}{4} = -1 \)
\( y = 0 \times \frac{1}{4} = 0 \)
So, \( D'(-1, 0) \)

For \( E(-4, 8) \):

\( x = -4 \times \frac{1}{4} = -1 \)
\( y = 8 \times \frac{1}{4} = 2 \)
So, \( E'(-1, 2) \)

For \( F(8, -4) \):

\( x = 8 \times \frac{1}{4} = 2 \)
\( y = -4 \times \frac{1}{4} = -1 \)
So, \( F'(2, -1) \)

For \( G(8, -8) \):

\( x = 8 \times \frac{1}{4} = 2 \)
\( y = -8 \times \frac{1}{4} = -2 \)
So, \( G'(2, -2) \)

Answer:

The coordinates after dilation are \( D'(-1, 0) \), \( E'(-1, 2) \), \( F'(2, -1) \), \( G'(2, -2) \)