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📐 Mathematics  ·  Straight Lines  ·  JEE

The foot of the perpendicular from (1, 2) to the line 3x + 4y − 5 = 0 is:

Answer: (7/25, 26/25).

  • A (7/25, 26/25)
  • B (1/5, 2/5)
  • C (−7/25, 26/25)
  • D (7/25, −26/25)

Correct answer: A. (7/25, 26/25)

Explanation: 3(1)+4(2)−5 = 6 and 3²+4² = 25. Foot = (1 − 3·6/25, 2 − 4·6/25) = (7/25, 26/25).

Slope as Rise over Runxy(x₁,y₁)(x₂,y₂)run = x₂−x₁rise = y₂−y₁m = rise/run = (y₂−y₁)/(x₂−x₁) = tanθ

The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.

Concept context

Points, lines, and curves on the Cartesian plane

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