Question

a triangle has vertices A(1,2),B(8,0),C(5,3),find the equation of the altitude from B to the opposite side.

Answer 1

The line AC has slope \(k = \frac{3 - 2}{5 - 1} = \frac{1}{4}\). The slope of the altitude is \(-1/k = -4\), so the altitude has the equation \(y = -4x + m\) for some constant \(m\). Knowing that the altitude passes through B we find that (by inserting x=8, y=0) \(0 = -4\cdot8 + m; m = 4\cdot8 = 32\). In conclusion, \(y = -4x + 32\)

Answer 2

Thank you very much Joel for your time and sharing your knowledge in helping me in my math problem. Your answer was very precise and easy to understand. Further thanks for reminding me of the important characteristic of perpendicular lines.