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AIEEE 2003

JEE Main 2003 Mathematics question on Straight Lines and Pair of Lines

Orthocentre of triangle with vertices (0,0)(0, 0), (3,4)(3, 4) and (4,0)(4, 0) is
  1. A.
    (3,54)\left(3, \dfrac{5}{4}\right)
  2. B.
    (3,12)(3, 12)
  3. C.
    (3,34)\left(3, \dfrac{3}{4}\right)
  4. D.
    (3,9)(3, 9)
Show answer and solution

Correct option: C

Solution

The altitude from (4,0) to side joining (0,0)-(3,4) has slope perpendicular to (4/3), so slope = -3/4. Line: y - 0 = -3/4(x - 4) → y = -3x/4 + 3.

The altitude from (3,4) to the x-axis (side joining (0,0)-(4,0)) is vertical: x = 3.

Substituting x = 3: y = -9/4 + 3 = 3/4.

Orthocentre is (3, 3/4).

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