Question

triangle abc has coordinates a (-1, 1), b (1, 1), and c (0, -1). triangle xyz will be a dilation of triangle abc with a scale factor of 3.
at what coordinates should point x, of triangle xyz, be plotted?
a. (-1, 3)
b. (-3, 1)
c. (3, -3)
d. (-3, 3)

Explanation:

Step1: Recall the dilation formula

For a dilation centered at the origin with scale factor \(k\), if a point \(P(x,y)\) is dilated, the new point \(P'(x',y')\) has coordinates \(x' = kx\) and \(y'=ky\). Here \(k = 3\).

Step2: Identify the original point

Assume the center of dilation is the origin. Looking at the graph, point \(A(-1,1)\) is likely to be the pre - image of point \(X\) (since the line from \(A\) to \(X\) passes through the origin and is part of the dilation transformation).

Step3: Apply the dilation formula

Using \(x=-1,y = 1,k = 3\), we get \(x'=3\times(-1)=-3\) and \(y'=3\times1 = 3\).

Answer:

D. \((-3,3)\)