Question

Line AB and line BC form a right angle at point B with points A(2,5) and B(8,3) . What is the equation of line BC ?

Answer 1

Answer: y = 3x - 21

Step-by-step explanation:

If the lines form a right angle, this means that they are perpendicular. Therefore, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other (in other words, their slopes multiply to -1).

The slope of AB is $\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}$. This means that the slope of BC is 3.

Substituting into point-slope form,

$y-3=3(x-8)\\\\y-3=3x-24\\\\\boxed{y=3x-21}$