The intersection of three lines x - y = 0 ,   x + 2 y = 3 and 2 x + y = 6 is a/an

The intersection of three lines x-y=0, x+2y=3 and 2x+y=6 is a/an
  1. Isosceles triangle
  2. Equilateral triangle
  3. Right angled triangle
  4. None of the above

Solution

.

L1:x-y=0

L2:x+2y=3

L3:2x+y=6

On solving L1 and L2:y=1 and x=1

On solving L1 and L3, we get

x=2

y=2

L2 and L3:

x+2y=3

2x+y=6

On solving L2 & L3, we get

x=3

y=0

AC=4+1=5

BC=4+1=5

AB=1+1=2

so it is an isosceles triangle

Asked in: JEE Main 2021 (26 Feb Shift 1)

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