Question

For what value of 'k' are the following points (7,-2), (5, 1), (3, k) collinear.

• A. 2
• B. 5
• C. 4
• D. 6

Answer 1

The correct option is C

4

The given three points will be collinear if the $\Delta$ formed by them has equal to zero area.
Let A(7, -2), B(5, 1) and C(3, k) be the vertices of a triangle
$\therefore$ The given points will be collinear, if ar$\left(\Delta ABC\right)=0$
or $7(1-k)+5(k+2)+3(-2-1)=0\Rightarrow 7-7k+5k+10+(-6)-3=0\Rightarrow 17-9+5k-7k=0\Rightarrow 8-2k=0\Rightarrow 2k=8\Rightarrow k=\frac{8}{2}=4$
The required value of $k=4$