Question

Anthony wants to find the value of k for which given points W(0,-2), I(2,0) and L(5,k) are collinear

Answer 1

Given:

The three points are W(0,-2), I(2,0) and L(5,k).

To find:

The value of k for which the given points are collinear.

Solution:

We know that, three points are collinear if the area of the triangle formed by these three points is 0.

$\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0$

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

The three points are W(0,-2), I(2,0) and L(5,k). So,

$0(0-k)+2(k-(-2))+5(-2-0)=0$

$0+2(k+2)+5(-2)=0$

$2k+4-10=0$

$2k-6=0$

Adding 6 on both sides, we get

$2k=6$

$k=\dfrac{6}{2}$

$k=3$

Therefore, the correct option is E.