Question

a square has vertices at a(-2,-2), b(-2,2), c(2,2), and d(2,-2). if it is dilated with a scale factor of 4 and the center of dilation is at (0,0), what are the coordinates of c? a. (-8,-8) b. (8,-8) c. (8,8) d. (-8,8)

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated with a scale - factor $k$ and center of dilation at the origin $(0,0)$, the new coordinates $(x',y')$ are given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Identify the original coordinates and scale - factor

The original coordinates of point $C$ are $(2,2)$ and the scale - factor $k = 4$.

Step3: Calculate the new coordinates

$x'=4\times2 = 8$ and $y'=4\times2 = 8$. So the coordinates of $C'$ are $(8,8)$.

Answer:

C. $(8,8)$