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. (3, -3)
b. (-3, 1)
c. (-1, 3)
d. (-3, 3)

Explanation:

Step1: Recall the dilation formula

For a dilation with scale factor \(k\) centered at the origin \((0,0)\), the formula for the coordinates of a point \((x,y)\) in the original figure and its image \((x',y')\) in the dilated figure is \(x' = kx\) and \(y'=ky\). Here \(k = 3\).

Step2: Apply the formula to point \(A(-1,1)\)

For point \(A(-1,1)\), when we dilate it with a scale factor \(k = 3\), we calculate \(x'=3\times(-1)=-3\) and \(y'=3\times1 = 3\).

Answer:

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