Question

in each of the following find the value of k for which the point are collinear (7,-2),(5,1),(3,k)

Answer 1

Hey there here is your answer!!!

If the points are collinear then-
1/2{x1(y2-y3)+x2(y3-y1)+x3(y1-y2)}=0
=>7(1-k)+5(k+2)+3(-2-1)=0
=>7-7k+5k+10-6-3=0
=>-2k+8=0
=>-2k=-8
=>2k=8
=>k=4

Hope it will help you:-)

Answer 2

1/2(x1(y2-y3)+x2(y3-y1)+x3(y1-y2)=0
 7(1-k)+5(k+2)+3(-2-1)=0*2
7-7k+5k+10-9=0
8-2k=0
-2k=-8
 k=8/2
 k=4
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