Question

1. a square with vertices (2,2), (2,6), (6,6), and (6,2) is dilated by a scale factor of 0.5 centered at the origin. what are the new coordinates of the vertex at (6,6)? a. (-3,-3) b. (12,12) c. (3,3) d. (1.5,1.5)

Explanation:

Step1: Recall dilation formula

When dilating a point $(x,y)$ centered at the origin with a scale factor $k$, the new - point $(x',y')$ is given by $(x',y')=(k\times x,k\times y)$.

Step2: Identify values

Here, $x = 6$, $y = 6$, and $k=0.5$.

Step3: Calculate new coordinates

$x'=0.5\times6 = 3$ and $y'=0.5\times6 = 3$. So the new coordinates are $(3,3)$.

Answer:

C. (3,3)