Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.
d((□, □))
e((□, □))
f((□, □))
g((□, □))

Explanation:

Step1: Find original coordinates

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

• \( D \): (0, -5)
• \( E \): (3, -4)
• \( F \): (0, 2)
• \( G \): (-3, -4)

Step2: Apply dilation rule

The rule for dilation centered at the origin with scale factor \( k \) is \( (x, y) \to (k \cdot x, k \cdot y) \). Here, \( k = 2 \).

For \( D(0, -5) \):

Multiply each coordinate by 2: \( (2 \cdot 0, 2 \cdot (-5)) = (0, -10) \), so \( D'(0, -10) \).

For \( E(3, -4) \):

Multiply each coordinate by 2: \( (2 \cdot 3, 2 \cdot (-4)) = (6, -8) \), so \( E'(6, -8) \).

For \( F(0, 2) \):

Multiply each coordinate by 2: \( (2 \cdot 0, 2 \cdot 2) = (0, 4) \), so \( F'(0, 4) \).

For \( G(-3, -4) \):

Multiply each coordinate by 2: \( (2 \cdot (-3), 2 \cdot (-4)) = (-6, -8) \), so \( G'(-6, -8) \).

Answer:

\( D'(0, -10) \)
\( E'(6, -8) \)
\( F'(0, 4) \)
\( G'(-6, -8) \)