Question

(4) If points (-2,-5) (2,-2) (8, a)
are collinear then a = ?​

Answer 1

Solution :-

Let :-

The points be A( -2 , -5 ), B( 2 , -2 ) and C( 8 , a ).

Given that, these points are collinear.

That is, area of triangle ABC 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 :-

$\bullet \sf \ x_1=-2 \ , \ y_1 = -5 \\\\\bullet \ x_2 = 2 \ , \ y_2 = -2 \\\\\bullet \ x_3 = 8 \ . \ y_3 = a$

$\longrightarrow \sf \dfrac{1}{2} \times [ \ -2(-2-a)+2(a-(-5))+8(-5-(-2)) \ ] = 0 \\\\\longrightarrow \dfrac{1}{2} \times [ \ -2(-2-a)+2(a+5)+8(-5+2) \ ] = 0 \\\\\longrightarrow \dfrac{1}{2} \times [ \ 4+2a+2a+10+ (8 \times -3 ) \ ] = 0 \\\\\longrightarrow \dfrac{1}{2} \times [ \ 4a+14-24 \ ] = 0 \\\\\longrightarrow \dfrac{1}{2} \times [ \ 4a-10 \ ] = 0 \\\\\longrightarrow 4a-10 = 0 \\\\\longrightarrow 4a = 10 \\\\\longrightarrow a = \dfrac{10}{4} \\\\\longrightarrow \bf a = 2.5$