Question

If the coordinates of the vertices of the triangle ABC be (-1, 6), (-3, -9), and (5, -8) respectively, then the equation of the median through C is
A) 13x-14y-47=0 B) 13x-14y+47=0 C) 13x+14y+47=0 D) 13x+14y-47=0

Answer 1

clearly the median passes through (5,-8) and the mid point joining (-1,6) and (-3,-9)
I. e (-2,-3/2)
by two point form we get
y+8 = -13/14(x-5)
14y+112 = -13x+65
13x+14y+40 = 0
hence this is the required equation

Answer 2

Given :  the coordinates of the vertices of the triangle ABC be (-1, 6), (-3, -9), and (5, -8) respectively

To Find : the equation of the median through C is

A) 13x-14y-47=0 B) 13x-14y+47=0 C) 13x+14y+47=0 D) 13x+14y-47=0

Solution:

A (-1, 6)

B (-3, -9)

C (5, -8)

mid point of AB   is F

A (-1, 6)  B (-3, -9)

( - 1 - 3)/2  , ( 6 - 9)/2

F = ( -2 , -3/2 )

C =  (5, -8)

Slope of CF  =  ( -8 -(-3/2))/(5 - (-2))

=   -13 /14

y -(-8)  = (-13/14) (x - 5)

=>14( y + 8  ) = -13 ( x - 5)

=> 14y + 112 = -13x + 65

=> 13x + 14y  +47 = 0

option C is correct

C) 13x+14y+47=0

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