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

Options

A. an isosceles triangle
B. an equilateral triangle
C. a scalene triangle
D. a right angled triangle

Answer

A

Explanation

Given lines are
x+y=0
5x+y=4
5x+y=4
x+5y =4
on Solving above equations pairwise , we get the following points of intersections
` A(1,-1) , B(2/3,2/3) , C (-1,1)`
Now, AB = `sqrt((2/3-1)^(2) + (2/3+1)^(2))`
=` sqrt(1/9+25/9)=sqrt(26/9) =sqrt26/3`
` BC= sqrt((-1-2/3)^(2)+(1-2/3)^(2))`
` sqrt(25/9 +1/9) +sqrt(26/9) = sqrt26/3`
and ` CA =sqrt((1+1)^(2)+(-1-1)^(2))=sqrt(4+4) =2sqrt2`
Here we see that AB =BC
Given lines form an isosceles triangle .