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📐 Mathematics  ·  Straight Lines  ·  JEE

The equation of the perpendicular from origin to the line x + y = 5 is:

Answer: y = x.

  • A y = x
  • B x = 5
  • C y = 5
  • D x + y = 0

Correct answer: A. y = x

Explanation: Line x + y = 5 has slope -1. Perpendicular slope = 1. Line through origin: y = x.

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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