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

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

Answer:

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