Question

problem 1
quadrilateral abcd is dilated with the origin as the center of dilation, moving point b onto point b. what is the scale factor of the dilation?
a(-2,3)
b(2,2)
c(1,-3)
d(-2,-1)
b(4,4)

Explanation:

Step1: Recall dilation formula

For a dilation with center at the origin $(0,0)$, if a point $(x,y)$ is dilated to $(x',y')$, the scale - factor $k$ is given by $x'=kx$ and $y' = ky$. Let the original point $B(2,2)$ and the dilated point $B'(4,4)$.

Step2: Calculate scale - factor for x - coordinate

Using the formula $x'=kx$, where $x = 2$ and $x'=4$. We solve for $k$: $k=\frac{x'}{x}=\frac{4}{2}=2$.

Step3: Calculate scale - factor for y - coordinate

Using the formula $y'=ky$, where $y = 2$ and $y'=4$. We solve for $k$: $k=\frac{y'}{y}=\frac{4}{2}=2$.

Answer:

$2$