Question

AB←→ and BC←→ form a right angle at point B. If A = (-3, -1) and

B = (4, 4), what is the equation of BC←→?




x + 3y = 16




2x + y = 12




-7x − 5y = -48




7x − 5y = 48

Answer 1

Long story short the answer your looking for is C. -7 - 5y= -48

Answer 2

Gradient of AB =
`(y_2-y_1)/(x_2-x_1) = (4-(-1))/(4-(-3)) = (4+1)/(4+3) =5/7`
Since AB and BC forms a right angle, this means that AB and BC are perpendicular.
For perpendicular lines, m2 = -1/m1; where m1 and m2 are the gradient of the two lines.
i.e. m2 = -1/(5/7) = -7/5
Therefore, the equation of BC is given by

`(y-y_1)/(x-x_1) =m_2 \\ (y-4)/(x-4) = -(7)/(5) \\ 7(x-4)=-5(y-4) \\ 7x-28=-5y+20 \\ -7x-5y=-48`