1983
JEE Main 1983 Mathematics question on Straight Lines and Pair of Lines
The straight lines
x+y=0,
3x+y−4=0,
x+3y−4=0 form a triangle which is
- A.
isosceles
- B.
equilateral
- C.
right angled
- D.
None of the above
Show answer and solution
Correct option: A
Solution
The three vertices are found by pairwise intersections: L1∩L2 gives (2,-2), L1∩L3 gives (-2,2), L2∩L3 gives (1,1).
Distances: between (2,-2) and (-2,2) = √(16+16) = 4√2; between (2,-2) and (1,1) = √(1+9) = √10; between (-2,2) and (1,1) = √(9+1) = √10.
Two sides are equal (both √10), so the triangle is isosceles.
[1983]
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