The point A divides the join of P(-5,1) and Q(3,5) in the ratio k:1. Find the two values of k for which the area of triangle ABC, where B is (1,5) and C is (7,-2), is equal to 2 units.

coordinates A can be given by using section formula for internal division, A= -5+3kk+1, 1+5kk+1and B 1,5, C 7,-2So area of triangle ABC, 12-5+3kk+17+1-2-1+5kk+1+71+5kk+1-5=2Solving we get, 14k-66k+1=4Taking positive sign, 14k-66=4k+410k = 70k=7Taking negative sign we get, 14k-66=-4k-418k = 62k = 6218=319

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