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)=(-2-1)/(4-(-4))=-(3)/(8)`

Now, we need to find a perpendicular slope:

`\begin{gathered} m\cdot m_(BC)=-1 \\ m=-(1)/(m_(BC)) \\ m=-(1)/(-(3)/(8)) \\ m=(8)/(3) \end{gathered}`

Now, using the point-slope equation:

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

Rewrite the previous equation in the standard form:

`\begin{gathered} (8)/(3)x-y=(1)/(3) \\ 8x-3y=1 \\ \end{gathered}`

Therefore, the answer is:

A = 8

B = -3

C = 1