Geometry - Equation of a line

Question

A triangle is formed from the points L(-3,6), N(3,2) and P(1,-8). Find the equation of the following lines: 

a) the median from N

b) the right bisector of LP

c) the altitude from N

Answer 1

The mid point of LP is (-1,-1). The median is (3/4)=(y-2)/(x-3).

The bisector is (2/7)=(y+1)/(x+1)

The altitude is (2/7)=(y-2)/(x-3)

Explanation:

The equation of the median is the equation of a line between (-1,-1) and (3,2).

The perpendicular bisector is the line through (-1,-1) with slope equal to the negative reciprocal of the slope of LP.

The altitude is the line through (3,2) with slope equal to the negative reciprocal of the slope of LP.