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Question 7
Find the value of m, if the points (5,1) (-2,-3) and (8,2m) are collinear
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Solution

Let A =(x1,y1) =(5,1)
B =(x2,y2) = (-2,-3)
C = (x3,y3) = (8,2m)
Since, the points A = (5,1),B = (-2,-3) and C = (8,2m) are collinear.
Area of ΔABC=012[x1(y2y3)+x2(y3y1)+x3(y1y2)]=012[5(32m)+(2)(2m1)+8(1(3))]=012(1510m4m+2+32)=012(14m+19)=0m=1914Hence, the required value of m is 1914.

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