A( 3 , 7 ) , B ( 5 , 11 ), C ( -2 , 8) are the vertices of ∆ ABC. AD is one of the median of the triangle. Find the equation of the median.

A( 3 , 7 ) , B ( 5 , 11 ), C ( -2 ,  8) are the vertices of ∆ ABC. AD is one of the median of the triangle. Find the equation of the median.

Solution:

Since, AD is the median,

∴ D is the mid point of Seg BC,

Now, By mid point formula

D = x1 + x2 , y1 + y2 2 2

D = 5 -  2  , 11 + 8 2 2

D = 3 , 19 2 2

Now, Median AD has, A = (3, 7) and D = (3/2 ,  19/ 2)

∴ Equation of Median AD by two point formulae,

x – x1 = y – y1 x1 – x2 y1 – y2

x – 3 = y –7 3 – 3/2 7 – 19/2

x – 3 = y –7 6 – 3 14 – 19 2 2

x – 3 = y –7 3 -5

∴ - 5x + 15 = 3y – 21

∴ - 5x – 3y + 15 + 21 = 0

∴ - 5x – 3y + 36 = 0

Changing the sign

∴ 5x + 3y – 36 = 0

Therefore, the equation of the median is 5x + 3y - 39 = 0