Question

given △abc, use a dilation with the center at the origin to make a similar triangle with side lengths three times as large. what are the coordinates of c of the image?
○ (-6, 3)
○ (-3, 6)
○ (3, -6)
○ (6, -3)

Explanation:

Step1: Find coordinates of C

From the graph, point C has coordinates \((2, -1)\).

Step2: Apply dilation with scale factor 3

Dilation with center at origin and scale factor \(k\) transforms \((x, y)\) to \((k x, k y)\). Here, \(k = 3\), so \(C'=(3\times2, 3\times(-1))=(6, -3)\).

Answer:

(6, -3)