Answer :

coordinates A can be given by using section formula for internal division,


A = ( , )


and B (1,5), C (7,−2)


Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3)


= |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|


Area of ∆ABC


= | (7) + 1(−2 ) + 7( - 5 ) |


But Area of ∆ABC = 2


| (7) + 1(−2 ) + 7( - 5 ) | = 2


Solving above we get,


| | = 4


Taking positive sign, 14k66=4k+4


10k = 70


k=7


Taking negative sign we get,


14k66=−4k4


18k = 62


k = =


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