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 the coordinates of point \(C\)

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

Step2: Use the dilation formula

For a dilation with center at the origin and scale factor \(k = 3\), the formula for the coordinates of a point \((x,y)\) in the original figure and its image \((x',y')\) is \(x'=k\times x\) and \(y'=k\times y\).
Substitute \(x = 2\), \(y=-1\) and \(k = 3\) into the formula:
\(x'=3\times2=6\)
\(y'=3\times(-1)=-3\)

So the coordinates of \(C'\) are \((6,-3)\).

Answer:

\((6, - 3)\)