Question

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

Answer 1

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

$A(7,-2)B(5,1)C(3,k)$ we have to find $k$

$x_1{y}_1$ $x_2{y}_2$ $x_3{y}_3$

The point are collinear if they lie on same line

$\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=0$

$\frac{1}{2}[7(1-k)+5(k+2)+3(-2-1)]=0$

$7-7k+5k+10-6-3=0$

$-2k+17-9=0$

$-2k=-8$

$k=\frac{8}{2}$

$k=4$