Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Find original coordinates

From the graph, original coordinates:

• \( B(0, -2) \)
• \( C(2, -1) \)
• \( D(0, 2) \)
• \( E(-2, -1) \)

Step2: Apply dilation (scale factor 4, center origin)

Dilation rule: \( (x, y) \to (4x, 4y) \)

• For \( B(0, -2) \):

\( B' = (4 \times 0, 4 \times -2) = (0, -8) \)

• For \( C(2, -1) \):

\( C' = (4 \times 2, 4 \times -1) = (8, -4) \)

• For \( D(0, 2) \):

\( D' = (4 \times 0, 4 \times 2) = (0, 8) \)

• For \( E(-2, -1) \):

\( E' = (4 \times -2, 4 \times -1) = (-8, -4) \)

Answer:

\( B'(0, -8) \)
\( C'(8, -4) \)
\( D'(0, 8) \)
\( E'(-8, -4) \)