If straight lines x + 3y = 4,,,3x + y = 4 and x +y = 0 form a triangle, then triangle is

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9.Straight Line

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If the straight lines $x + 3y = 4,\,\,3x + y = 4$ and $x +y = 0$ form a triangle, then the triangle is

A

scalene

B

equilateral triangle

C

isosceles

D

right angled isosceles

(AIEEE-2012)

Solution

Let equation of $AB:x+3y=4$

Let equation of $BC:3x+y=4$

Let equation of $CA:x+y=0$

Now,By solving these equations we get

$A=(-2,2)$, $B=(1,1)$ and $C=(2,-2)$

Now, $AB = \sqrt {9 + 1} = \sqrt {10} $,

$BC = \sqrt {1 + 9} = \sqrt {10} $

and $CA = \sqrt {16 + 16} = \sqrt {32} $

Since, length of $AB$ and $BC$ are same therfore triangle is isosceles.

Standard 11

Mathematics

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