A( -1 , 3) B ( 5 , 2 ) and C ( 3, - 2) are the vertices of triangle ABC find the equation of median through A
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Given,
A(-1,3) , B(5,2), C(3,-2)
Mid point of BC (Let's name it as D)
= 5+ 3 2 - 2
------- , -------
2 2
∴ D = (4,0)
Now,
Median through A = Line passing through A and D
Using the formula,
y2-y1
(y-y1) = ---------- × (x-x1)
x2-x1
A(-1,3) , D(4,0)
⇒ 0 - 3
y - 3 = ----------- × x +1
4 + 1
(y - 3) × 5 = -3(x+1)
5y - 15 = -3x - 3
3x + 5y - 12 = 0
∴ The equation of the median passing through A is 3x + 5y - 12 = 0.