Question

1. a square with vertices at (1,1), (1,3), (3,3), and (3,1) is dilated with a scale factor of 2 using the origin as the center. what are the coordinates of the new vertices?

a. (1,2), (1,4), (3,4), (3,2)
b. (0.5,0.5), (0.5,1.5), (1.5,1.5), (1.5,0.5)
c. (2,2), (2,4), (4,4), (4,2)
d. (2,2), (2,6), (6,6), (6,2)

Explanation:

Step1: Recall dilation formula

When dilating a point $(x,y)$ with a scale - factor $k$ and the origin as the center of dilation, the new point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Apply dilation to each vertex

The original vertices of the square are $(1,1),(1,3),(3,3),(3,1)$. With a scale - factor $k = 2$, for the point $(1,1)$: $(x',y')=(2\times1,2\times1)=(2,2)$; for the point $(1,3)$: $(x',y')=(2\times1,2\times3)=(2,6)$; for the point $(3,3)$: $(x',y')=(2\times3,2\times3)=(6,6)$; for the point $(3,1)$: $(x',y')=(2\times3,2\times1)=(6,2)$.

Answer:

d. $(2,2),(2,6),(6,6),(6,2)$