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1995

JEE Main 1995 Mathematics question on Straight Lines and Pair of Lines

The orthocentre of the triangle formed by the lines xy=0xy = 0 and x+y=1x + y = 1, is
  1. A.
    (12,12)\left(\dfrac{1}{2}, \dfrac{1}{2}\right)
  2. B.
    (13,13)\left(\dfrac{1}{3}, \dfrac{1}{3}\right)
  3. C.
    (0,0)(0, 0)
  4. D.
    (14,14)\left(\dfrac{1}{4}, \dfrac{1}{4}\right)
Show answer and solution

Correct option: C

Solution

xy = 0 represents the x-axis and y-axis. These two lines are perpendicular to each other, meeting at the origin (0,0). Since the triangle has a right angle at the origin, the orthocentre of a right-angled triangle is always at the vertex where the right angle occurs, which is (0,0).

[1995]

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