Question

Find the value of ${}^{\prime }{k}^{\prime }$ for the points $(7,-2),(5,1),(3,k)$ are collinear.

Answer 1

If the points are collinear, then the area of the triangle will be O.

$(7,-2),(5,1),(3,k)$

$|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0$

$|7(1-k)+5(k+2)+3(-2-1)|=0$

$|7-7k+5k+10-9|=0$

$|17-9-2k|=0$

$8-2k=0$

$2k=8$

$k=4$.