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In a DeltaABC, A = (2,3) and medians thr...

In a `DeltaABC, A = (2,3)` and medians through B and C have equations `x +y - 1 = 0` and `2y - 1 = 0`
Equation of median through A is

A

`x +y = 4`

B

`5x - 3y = 1`

C

`5x +3y = 1`

D

`5x = 3y`

Text Solution

Verified by Experts

The correct Answer is:
B

Centroid is the point of intersection of `x +y -1 = 0, 2y -1 = 0` or `D ((1)/(2),(1)/(2))`
Slope of AD is `(3-(1)/(2))/(2-(1)/(2)) =(5)/(3)`
`:.` Equation of AD is `y - 3 = (5)/(3) (x-2)` or `5x - 3y - 1 = 0`
A point of `CF: 2y - 1 = 0` is `(alpha, (1)/(2))`
Let this be the midpoint of AB.
`:.` B is `(2alpha -2,-2)` which lies on median `BE: x +y - 1 = 0`
`:. 2alpha -2-2-1 = 0 :. alpha =(5)/(2)`
`:. B (3,-2)`
G divides CF in 2:1
`:. C = ((-7)/(2),(1)/(2))`
`:.` Equation of BC is `(y+2)/((1)/(2)+2) = (x-3)/((-7)/(2)-3)`
or `(y+2)/(5) =(x-3)/(-13)`
or `5x +13y +11 = 0`
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