A point `A` divides the join of `P(-5,1)` and `Q(3,5)` in the ratio `k :1` . Then the integral value of `k` for which the area of ` A B C ,` where `B` is `(1,5)` and `C` is `(7,-2)` , is equal to 2 units in magnitude is___

Explanation

Given, the point A divides the join of `P(−5,1)` and `Q(3,5)` in the ratio `k:1`


By using section formula for internal division coordinates of `A` is,


`A=((3k−5)/(k+1)​,(5k+1)/(k+1)​) `and `B(1,5),C(7,−2)`


So area of `DeltaABC`

=`1/2​|​(3k−5)/(k+1)(5+2)+1(−2−(5k+1)/(k+1))+7((5k+1)/(k+1)−5)|​=2`

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