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Question

The straight lines x+y=0,5x+y=4 and x+5y=4 form


A

an isosceles triangle

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B

an equilateral triangle

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C

a scalene triangle

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D

a right angles triangle

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Solution

The correct option is A

an isosceles triangle


Explanation for the correct option:

Compute the required term:

Given x+y=0..(i)

5x+y=4..(ii)

x+5y=4(iii)

Solving (i) and (ii), we get x=1,y=-1

So A=(1,-1)

Solving (ii) and (iii), we get x=23,y=23

So B=(23,23)

Solving (i) and (iii), we get x=-1,y=1

So C=(-1,1)

AB=(x2x1)2+(y2y1)2 (distance formula)

=263

Similarly BC=263

AC=22

Here AB=BC

Here the two sides of the triangle are equal, so the triangle is isosceles.

Hence option A is the correct answer.


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