Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin. graph with coordinate grid, vertices e, f, g, h, and boxes for e, f, g, h coordinates

Explanation:

Step1: Find original coordinates

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

• \( E(-2, -4) \)
• \( F(-1, -4) \)
• \( G(-1, -2) \)
• \( H(-2, -2) \)

Step2: Apply dilation formula

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 \( E(-2, -4) \):
\( E' = (2 \cdot (-2), 2 \cdot (-4)) = (-4, -8) \)

For \( F(-1, -4) \):
\( F' = (2 \cdot (-1), 2 \cdot (-4)) = (-2, -8) \)

For \( G(-1, -2) \):
\( G' = (2 \cdot (-1), 2 \cdot (-2)) = (-2, -4) \)

For \( H(-2, -2) \):
\( H' = (2 \cdot (-2), 2 \cdot (-2)) = (-4, -4) \)

Answer:

\( E'(-4, -8) \)
\( F'(-2, -8) \)
\( G'(-2, -4) \)
\( H'(-4, -4) \)