Question

The equation of the median of the triangle with vertices (4 3) (-2 3) (1-2) passing through (-2,3)
1) 5x+9y+17=0
2) 9x-5y-11=0
3) 5x+9y-17=0
4) 5x-9y+13=0
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Answer 1

Answer:

the answer is 2) 9x-5y-11

Answer 2

We have to find the median of the triangle with vertices (4, 3) , (-2, 3) and (1, -2) passing through (-2, 3).

solution : let A = (4, 3) , B = (-2, 3) and C = (1, -2)

if a median is passing through point B, it must meet at the middle point of side CA.

let E is the midpoint of side CA.

from midpoint section formula, (x , y) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

here (x₁ , y₁) = (4, 3) and (x₂ , y₂) = (1, -2) and (x, y) = E

∴ point E = [(4 + 1)/2, (3 - 2)/2 ] = (5/2, 1/2)

now slope of BE = difference of ordinate/difference of abscissa

= {5/2 - (-2)}/{1/2 - 3}

= (9/2)/(-5/2)

= -9/5

now equation of median BE is ..

(y - 5/2) = -9/5 (x - 1/2)

⇒5y - 25/2 = -9x + 9/2

⇒5y + 9x - (25 + 9)/2 = 0

⇒9x + 5y - 17 = 0

Therefore the equation of median passing through (-2, 3) is 9x + 5y - 17 = 0. i.e., correct option is (3)