Median and Altitude of a 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

I will give you detailed solution of part a). For parts b) and c) you need to calculate the lines using the given instructions.

a) median from N

   Let M is the median of side LP. The coordinates of M are average of the coordinates of L and P.

   M = ((-3+1)/2, (6-8)/2)

      = (-1, -1).

 

Slope of the line MN is

m_MN =(-1-2)/(-1-3)

        =-3/-4=3/4.

 

We can use one of the points, M or N to write the equation of a line using point-slope formula

y - y₁= m(x - x₁)

If the point is M:

y - (-1) = 3/4(x - (-1)).

y +1 = 3/4x +3/4

y  = 3/4x - 1/4.

 

b) right bisector of LP will pass point M(-1, -1)

    Calculate the slope of the line LP. The perpendicular bisector line will have slope which is negative reciprocal (for example 3/4 and -4/3 are.)

 

Then use the process in part a) to write the line.

 

 

c) The altitude from N will have the same slope as the perpendicular bisector line found in part b) and will pass through point N.

 

Do you still have questions?