Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.
graph with coordinate grid and vertices p, q, r, s marked; below the graph: p((box, box)) q((box, box)) r((box, box)) s((box, box))

Explanation:

Step1: Find original coordinates

From the graph:

• \( P(0, -3) \)
• \( Q(2, 0) \)
• \( R(0, 1) \)
• \( S(-2, 0) \)

Step2: Apply dilation rule

Dilation centered at origin with scale factor \( k \) transforms \( (x, y) \) to \( (k \cdot x, k \cdot y) \). Here, \( k = 3 \).

For \( P(0, -3) \):

\( P' = (3 \cdot 0, 3 \cdot (-3)) = (0, -9) \)

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

\( Q' = (3 \cdot 2, 3 \cdot 0) = (6, 0) \)

For \( R(0, 1) \):

\( R' = (3 \cdot 0, 3 \cdot 1) = (0, 3) \)

For \( S(-2, 0) \):

\( S' = (3 \cdot (-2), 3 \cdot 0) = (-6, 0) \)

Answer:

\( P'(0, -9) \)
\( Q'(6, 0) \)
\( R'(0, 3) \)
\( S'(-6, 0) \)