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Question

Find the value of m if the points (5,1),(2,3) and (8,2m) are collinear.

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Solution

Points A, B, C will be collinear if the area of ΔABC=0.
i.e., 12[x1(y2y3)+x2[y3y1)+x3(y1y2)]=0

12[5(32m)2(2m1)+8(1+3)=0

1510m4m+2+32=0

14m15+34=0

14m+19=0

14m=19

m=1914

Hence, the rquired value of m=1914.

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