Question

A triangle has vertices at A(1, 2), B(3, 4) and C(-2, - 5). Then its median cannot be represented by
the line is
(a)5x - y = 3

(b)I lx-7 y = 5

(c)2x - y = 1

(d) 4x- 2y=4​

Answer 1

AD, BE & CF will be the medians.

therefore, D,E & F are the mid pt. of AB, BC & CA

now, the coordinates of D are :-

[{3+(-2)}/2],[{4+(-5)}/2] = (1/2,-1/2)

similarly coordinates of E&F are :-

E = (-2+1)/2,(-5+2)/2 = (-1/2,-3/2)

F = (1+3)/2,(2+4)/2 = (2,3)

Now,

equation of median AD is :-

{y-(-1/2)}/{2-(-1/2)} = (x-1/2)/(1-1/2)

(y+1/2)/(5/2) = (x-1/2)/(1/2)

(1/2)*(2y+1)/2 = (2x-1)/2*(5/2)

2y+1 = 10x-5

5x-y = 3.

similarly, equation of median BE & CF is :-

BE » (y+3/2)/(4+3/2) = (x+1/2)/(3+1/2)

(y+3/2)/(11/2) = (x+1/2)/(7/2)

14y+21 = 22x+11

4y-22x = -10

7y-11x = -5

11x-7y = 5.

CF » (y-3)/(-5-3) = (x-2)/(-2-2)

(y-3)/(-8) = (x-2)/(-4)

y-3 = 2x-4

2x-y = 1.

therefore, 4x-2y = 4 can not be represented by the median of the given triangle.