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Two Point Form of a Line

The sides of ...

Question

The sides of a triangle are the straight lines $x + y = 1; 7 y = x$ and $\sqrt{3} y + x = 0$ . Then which of the following is an interior point of the triangle?

A

Circumcentre

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B

Centroid

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C

Incentre

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D

Orthocentre

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Solution

The correct option is A Circumcentre
Given the three sides of a triangle,
$x + y = 1 7 y = x \Rightarrow y = \frac{x}{7} \sqrt{3 y} + x = 0 y = \frac{- x}{\sqrt{3}}$
From the graph,circumcenter and orthocentre lies outside.Incenter lies inside.

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