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📐 Mathematics  ·  Straight Lines  ·  JEE

The point dividing (2,3) and (8,9) internally in ratio 1:2 is:

Answer: (4,5).

  • A (4,5)
  • B (5,6)
  • C (6,7)
  • D (3,4)

Correct answer: A. (4,5)

Explanation: Section formula: x = (1×8+2×2)/(1+2) = 12/3 = 4; y = (1×9+2×3)/3 = 15/3 = 5. Point = (4,5).

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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