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📐 Mathematics  ·  Straight Lines  ·  JEE

Three points (1,1), (2,3), (3,5) are:

Answer: Collinear (on same line).

  • A Vertices of a triangle
  • B Collinear (on same line)
  • C Form a right angle
  • D Equidistant from origin

Correct answer: B. Collinear (on same line)

Explanation: Slope from (1,1) to (2,3) = 2; from (2,3) to (3,5) = 2. Equal slopes so collinear.

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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