Question

for what values of k are the points (8,1),(3,_2k) and (k,_5) collinear​

Answer 1

Since the points are collinear, their area must be equal to zero.

Therefore:-

=>1/2 [x1(y2-y3) + x2 (y3-y1) + x3 (y1-y2)] =0

=>1/2 [8 (-2k+5) +3 (-5-1) +k (1+2k)]=0

=> 1/2 [-16k+40 +3 (-6) + k +2k^2]=0

=> 1/2 [-15k+40-18+2k^2]=0

=> 1/2 [ -15k+32+2k^ 2]=0

=> -15k + 32 +2k^2 =0

=> 2k^2-15k+32 =0

You can solve the equation ahead.

Hope it helped:)