for what values of k are the points [8,1] [3,-2k] [k,-5] are colinear
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points are colinear when area if triangle equals zero
area of triangle=1/2 {8 (-2k+5)+3 (-5-1)+k (1+2k)}
8 (-2k+5)-18+k (1+2k)=0
-16k+40-18+k+2k^2=0
2k^2-15k+22=0
use quadratic formula
k=2,11/2
area of triangle=1/2 {8 (-2k+5)+3 (-5-1)+k (1+2k)}
8 (-2k+5)-18+k (1+2k)=0
-16k+40-18+k+2k^2=0
2k^2-15k+22=0
use quadratic formula
k=2,11/2
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