Triangle with Points

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

For the median from N:

1. determine the midpoint of LP (call that point M)
2. determine the slope of NM
3. use point-slope to write the equation of the median (convert to slope-intercept if you want)

For the perpendicular bisector of LP:

1. You already have the midpoint of LP (point M)
2. determine the slope of LP
3. the slope of the perpendicular bisector is the negative reciprocal of the slope of LP
4. use point-slope to write the equation of the perpendicular bisector (convert to slope-intercept)

For the altitude from N:

1. we already have the slope of LP and the slope of any perpendicular to LP
2. use point-slope to write the equation of the altitude from N where the point to use is N.

desmos.com/calculator/ifvysy0r5c

The above graph provides the details.