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📐 Mathematics  ·  Straight Lines  ·  JEE

Find the area of triangle with vertices (0,0), (3,0), (0,4).

Answer: 6.

  • A 6
  • B 12
  • C 8
  • D 10

Correct answer: A. 6

Explanation: Area = (1/2)|x<sub>1</sub>(y<sub>2</sub>-y<sub>3</sub>) + x<sub>2</sub>(y<sub>3</sub>-y<sub>1</sub>) + x<sub>3</sub>(y<sub>1</sub>-y<sub>2</sub>)| = (1/2)|0+3(0-0)+0(0-0)| hmm. Area = (1/2) × base × height = (1/2) × 3 × 4 = 6.

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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