Question

graph the image of δklm after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Identify coordinates of K, L, M

From the graph, \( K(-3, 0) \), \( L(-3, 3) \), \( M(3, -2) \) (assuming grid units, correcting possible typos in original labels).

Step2: Apply dilation (scale factor 3, origin)

Dilation rule: \( (x, y) \to (3x, 3y) \).

• For \( K(-3, 0) \): \( (3 \times -3, 3 \times 0) = (-9, 0) \)
• For \( L(-3, 3) \): \( (3 \times -3, 3 \times 3) = (-9, 9) \)
• For \( M(3, -2) \): \( (3 \times 3, 3 \times -2) = (9, -6) \)

Step3: Plot new points

Plot \( K'(-9, 0) \), \( L'(-9, 9) \), \( M'(9, -6) \) and connect to form \( \triangle K'L'M' \).

Answer:

The dilated triangle has vertices at \( K'(-9, 0) \), \( L'(-9, 9) \), \( M'(9, -6) \). (Graph by plotting these points and connecting them.)