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

A. K=-3

B. K=1/3

C. K=1/2

D. K=2

E. K=3

F. K=-1/3

Respuesta :

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.

[tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0[/tex]

[tex]x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0[/tex]

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

[tex]0(0-k)+2(k-(-2))+5(-2-0)=0[/tex]

[tex]0+2(k+2)+5(-2)=0[/tex]

[tex]2k+4-10=0[/tex]

[tex]2k-6=0[/tex]

Adding 6 on both sides, we get

[tex]2k=6[/tex]

[tex]k=\dfrac{6}{2}[/tex]

[tex]k=3[/tex]

Therefore, the correct option is E.

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