Question

For what value of a the point (a, 1),(1, -1) and(11, 4) are collinear?

Answer 1

The value of "a is equal to 5".

Step-by-step explanation:

Here, $x_{1} =a, y_{1} =1$, $x_{2} =1, y_{2} =-1$ and $x_{3} =11, y_{3} =4$

To find, the value of a = ?

We know that,

The condition of the three points are col-linear, the area of triangle = 0.

$x_{1}(y_{2}-y_{2})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})=0$

∴ a( - 1 - 4) + 1(4 - 1) + 11(1 + 1) = 0

⇒ a( - 5) + 1(3) + 11(2) = 0

⇒ - 5a + 3 + 22 = 0

⇒ - 5a + 25= 0

⇒ - 5a = - 25

⇒ a = 5

Thus, the value of "a is equal to 5".