Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.
graph with coordinate plane, points j, k, l, and input boxes for j(□, □), k(□, □), l(□, □)

Explanation:

Step1: Find original coordinates

From the graph, we identify the original coordinates:

• \( J(-3, 1) \)
• \( K(-3, 2) \)
• \( L(-2, 2) \)

Step2: Apply dilation rule

The rule for dilation centered at the origin with scale factor \( k \) is \( (x, y) \to (kx, ky) \). Here, \( k = 3 \).

For \( J(-3, 1) \):
\( J' = (3 \times -3, 3 \times 1) = (-9, 3) \)

For \( K(-3, 2) \):
\( K' = (3 \times -3, 3 \times 2) = (-9, 6) \)

For \( L(-2, 2) \):
\( L' = (3 \times -2, 3 \times 2) = (-6, 6) \)

Answer:

\( J'(-9, 3) \)
\( K'(-9, 6) \)
\( L'(-6, 6) \)