Question

find the coordinates of point ( c ) by dilating ( \triangle abc ) by a scale factor of 2 with a center of dilation at the origin. enter your response as an ordered pair.

Explanation:

Step1: Find the coordinates of point \( C \)

From the graph, the coordinates of point \( C \) are \( (3,0) \).

Step2: Apply the dilation formula

The formula for dilation with a scale factor \( k \) and center at the origin \((x,y)\to(kx,ky)\). Here \( k = 2\), \(x = 3\), \(y=0\).
Substitute into the formula: \(x'=2\times3\), \(y'=2\times0\).
So \(x' = 6\), \(y'=0\).

Answer:

\((6,0)\)