Question

given \\( \triangle 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 the coordinates of point C

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

Step2: Apply the dilation rule

The dilation rule with a scale factor \( k = 3 \) and center at the origin \((x,y)\to(kx,ky)\).
Substitute \( x = 2 \) and \( y=-1 \) into the rule:
\( x'=3\times2 = 6 \) and \( y'=3\times(-1)=-3 \)

Answer:

\((6, - 3)\) (the fourth option)