If the points $ (-8,4),(-2,4) $ and $ (5, a) $ are collinear points, find the value of $ a $.

Given:

Points $(-8, 4), (-2, 4)$ and $(5, a)$ are collinear.

To do:

We have to find the value of $a$.

Solution:

Let $A (-8, 4), B (-2, 4)$ and $C (5, a)$ be the vertices of $\triangle ABC$.

We know that,

Area of a triangle with vertices $(x_1,y_1), (x_2,y_2), (x_3,y_3)$ is given by, 

Area of $\Delta=\frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]$

Therefore,

Area of triangle \( ABC=\frac{1}{2}[-8(4-a)+-2(a-4)+5(4-4)] \)

\( 0=\frac{1}{2}[-32+8a-2a+8+5(0)] \)

\( 0(2)=(6a-24) \)

\( 6a=24 \)

\( a=\frac{24}{6} \)

\( a=4 \)

The value of $a$ is $4$.  

Tutorialspoint

Updated on: 10-Oct-2022

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