Question

Please answer this questions and identify A, B, and C

Answer 1

First, we need to find the slope of the segment BC:

$m_{BC}=\frac{-2-1}{4-(-4)}=-\frac{3}{8}$

Now, we need to find a perpendicular slope:

$\begin{gathered} m\cdot m_{BC}=-1 \\ m=-\frac{1}{m_{BC}} \\ m=-\frac{1}{-\frac{3}{8}} \\ m=\frac{8}{3} \end{gathered}$

Now, using the point-slope equation:

$\begin{gathered} y-y1=m(x-x1) \\ where: \\ m=\frac{8}{3} \\ (x1,y1)=(2,5) \\ so: \\ y-5=\frac{8}{3}(x-2) \\ y-5=\frac{8}{3}x-\frac{16}{3} \\ y=\frac{8}{3}x-\frac{1}{3} \end{gathered}$

Rewrite the previous equation in the standard form:

$\begin{gathered} \frac{8}{3}x-y=\frac{1}{3} \\ 8x-3y=1 \\ \end{gathered}$

Therefore, the answer is:

A = 8

B = -3

C = 1