Question

a triangle △ghi has vertices g(2,2),h(6,2),i(4,6). its image after dilation has vertices g(4,4),h(12,4),i(8,12). what is the scale factor?
a. 1.5
b. 2
c. 1
d. $\frac{1}{2}$

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ for a dilation of a point $(x,y)$ to $(x',y')$ is given by $k=\frac{x'}{x}=\frac{y'}{y}$ (assuming $x
eq0$).

Step2: Use one of the points

Let's use point $G(2,2)$ and its image $G'(4,4)$. Calculate the scale factor using the $x$ - coordinates: $k = \frac{x_{G'}}{x_{G}}=\frac{4}{2}=2$. Calculate the scale factor using the $y$ - coordinates: $k=\frac{y_{G'}}{y_{G}}=\frac{4}{2}=2$.

Answer:

B. 2