select the correct answer.\nthe slope of $overleftrightarrow{fg}$ is 4. point f is located at (2,3). which…

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $m = 4$, $x_1=2$, and $y_1 = 3$. Let the coordinates of point $G$ be $(x_2,y_2)$. So $4=\frac{y_2 - 3}{x_2 - 2}$.

Step2: Test option A

For point $A(6,4)$: $\frac{4 - 3}{6 - 2}=\frac{1}{4}\neq4$.

Step3: Test option B

For point $B(3,7)$: $\frac{7 - 3}{3 - 2}=\frac{4}{1}=4$.

Step4: Test option C

For point $C(6,7)$: $\frac{7 - 3}{6 - 2}=\frac{4}{4}=1\neq4$.

Step5: Test option D

For point $D(8,12)$: $\frac{12 - 3}{8 - 2}=\frac{9}{6}=\frac{3}{2}\neq4$.

Answer:

B. $(3,7)$