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 - point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Identify the values of $x$, $y$, and $k$

The coordinates of point $C$ are $(2,2)$, so $x = 2$, $y = 2$, and the scale factor $k = 4$.

Step3: Calculate the new coordinates

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

Answer:

C. $(8,8)$