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, 1)

b. (3, -3)

c. (-1, 3)

d. (-3, 3)

Explanation:

Step1: Recall dilation rule

To dilate a point \((x,y)\) with a scale factor \(k\), we multiply each coordinate by \(k\), so the new coordinates are \((kx,ky)\).

Step2: Identify corresponding point

Point \(X\) in triangle \(XYZ\) corresponds to point \(A\) in triangle \(ABC\). The coordinates of \(A\) are \((-1,1)\).

Step3: Apply dilation

Using the dilation rule with \(k = 3\), we calculate the coordinates of \(X\) as follows:
For the \(x\)-coordinate: \(-1\times3=-3\)
For the \(y\)-coordinate: \(1\times3 = 3\)
So the coordinates of \(X\) are \((-3,3)\).

Answer:

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