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In a triangle A B C , side A B has equat...

In a triangle `A B C ,` side `A B` has equation `2x+3y=29` and side `A C` has equation `x+2y=16.` If the midpoint of `B C` is (5, 6), then find the equation of `B Cdot`

Text Solution

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Vertex C lies on the line x+2y = 16.
So, let point C be (16-2t,t).
D(5,6) is midpoint of BC.
So, point B is (2t-6, 12-t)
Point B lies on the line 2x+3y-29 = 0
`therefore 2(2t-6) +3(12-t)-29= 0`
`rArr t=5`
Hence, point B is (4,7)
Therefore, equation of line BC is
`y-7 = (6-7)/(5-4)(x-4)`
or x+y = 11
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