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📐 Mathematics  ·  Straight Lines  ·  JEE

Two perpendicular lines have slopes m<sub>1</sub> and m<sub>2</sub> where:

Answer: m 1 × m 2 = -1.

  • A m<sub>1</sub> = m<sub>2</sub>
  • B m<sub>1</sub> + m<sub>2</sub> = 0
  • C m<sub>1</sub> × m<sub>2</sub> = -1
  • D m<sub>1</sub> × m<sub>2</sub> = 1

Correct answer: C. m<sub>1</sub> × m<sub>2</sub> = -1

Explanation: Perpendicular lines: m<sub>1</sub> × m<sub>2</sub> = -1. If one slope is 2, the perpendicular slope is -1/2.

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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