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 in a coordinate - plane can be found by comparing the coordinates of a pre - image point $(x,y)$ and its image point $(x',y')$ using the formula $k=\frac{x'}{x}$ (or $k = \frac{y'}{y}$) for non - zero $x$ (or $y$). Let's use the $x$ - coordinates of point $G$ and $G'$.

Step2: Calculate the scale factor

For point $G(2,2)$ and $G'(4,4)$, we calculate the scale factor $k$ using the $x$ - coordinates. $k=\frac{x_{G'}}{x_{G}}=\frac{4}{2}=2$. We can also check using the $y$ - coordinates: $k=\frac{y_{G'}}{y_{G}}=\frac{4}{2}=2$. Let's double - check with another point, say point $H$. For point $H(6,2)$ and $H'(12,4)$, using the $x$ - coordinates, $k=\frac{x_{H'}}{x_{H}}=\frac{12}{6}=2$.

Answer:

B. 2