Maths / Coordinate Geometry / Area of Triangle Using Coordinate

QUESTION

Prove that the points (2,-2), (-3,8) and (-1,4) are collinear.

EXPLANATION
Explain TypeExplanation Content
Text

Let $\Delta$  be the area of the triangle formed by the given points

We have,

$\therefore \: \: \: \: \: \: \Delta =\frac {1}{2}\left | \left \{ 2\times 8+(-3)\times4+(-1)\times(-2) \right \}-\left \{ (-3)\times(-2)+(-1)\times8+2\times4 \right \} \right |$

$\Rightarrow \: \: \: \: \: \: \Delta =\frac {1}{2}\left | (16-12+2)-(6-8+8) \right |$

$\Rightarrow \: \: \: \: \: \: \Delta =\frac {1}{2}\left | 6-6 \right |=0$

Hence, given points are collinear.

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