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📐 Mathematics  ·  Straight Lines  ·  JEE

The point (2,3) divides line segment from (0,0) to (6,9) in ratio:

Answer: 1:2.

  • A 1:2
  • B 2:1
  • C 1:3
  • D 3:1

Correct answer: A. 1:2

Explanation: Section formula: x = mx2/(m+n) (for internal from origin). 2 = 6m/(m+n). 2m+2n=6m, 2n=4m, m/n = 1/2. Ratio = 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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