For what values of k are the points (8,1) , (3,-2k) and (k,-5) collinear ?
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Let A(x1=8,y1=1),B(x2=3,y2=−2k) & C(x3=k,y3=−5)
be the given point
The given points are collinear if
x1(y2−y3)+x2(y3−y1)+x3(y1−y2)=0
on puting values we get
8(−2k+5)+3(−5−1)+k(1+2k)=0
−16k+40−18+k+2k2=0
2x2−15x+22=0
2k2−4k−11k+22=0
2k(k−2)−11(k−2)=0
(2k−11)(k−2)=0
k=2
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