Question

using dilations to make similar figures
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 formula

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

Answer:

\( (6,-3) \) (Option D)