Question

If the points (0, 2) (1, x) (3, 1) are collineae, then x=

Answer 1

SOLUTION :-

Let the points be,

• A = ( 0 , 2 )

• B = ( 1 , x )

• C = ( 3, 1 )

Given that,

These points are collinear.

That is, area of the triangle is equal to zero.

$\boxed{\bf Area \ of \ triangle = \dfrac{1}{2} \times [ \ x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(Y_{1}-y_{2}) \ ] }$

Here,

$\bullet \sf \ x_{1}=0 \ , \ y_{1}= 2 \\\\\bullet \ x_{2}= 1 \ , \ y _{2}= x \\\\\bullet \ x_{3} = 3 \ , \ y_{3} = 1$

$\longrightarrow \sf \dfrac{1}{2}\times [ \ 0\times (x-1)+1\times (1-2) + 3\times (2-x) \ ] =0 \\\\\longrightarrow \dfrac{1}{2} \times [ \ -1+6-3x \ ] = 0 \\\\\longrightarrow \dfrac{1}{2} \times [ \ 5-3x \ ] = 0 \\\\\longrightarrow 5 -3x = 0 \\\\\longrightarrow -3x = -5 \\\\\longrightarrow x = \dfrac{5}{3}$

$\bf \ Value \ of \ x = \dfrac{5}{3}$