Coordinate Geometry

Coordinate geometry links algebra and geometry using the x-y plane. In this topic you will learn to plot points, find lengths and midpoints, calculate gradients, and write equations of straight lines. All work is for O-Level syllabus.

  • Distance and midpoint
  • Gradient of a line
  • Equation of a straight line
  • Parallel and perpendicular lines

Lessons for Coordinate Geometry

Length of a Line and Midpoint

Distance between two pointsFor points A(x1, y1) and B(x2, y2):AB = √[(x2 - x1)2 + (y2 - y1)2]This comes from …

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Gradient of a Straight Line

What is gradient?Gradient measures steepness: gradient = rise / runFor points A(x1, y1) and B(x2, y2):m = (y2 - y1) …

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Equation of a Straight Line

Main form: y = mx + cm = gradient, c = y-intercept (where line cuts y-axis)Finding the equationMethod 1: If …

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Parallel and Perpendicular Lines

Parallel linesParallel lines have the same gradient.If y = 2x + 3, then a parallel line could be y = …

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Exercises for Coordinate Geometry

Distance and midpoint

Calculate:Distance between (0, 0) and (3, 4)Distance between (-1, 2) and (2, 6)Midpoint of (2, 5) and (8, 1)Midpoint of …

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Find the gradient

Find the gradient of the line through:(0, 0) and (2, 6)(1, 5) and (4, -1)(-2, 3) and (3, 3)(4, 1) …

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Find the equation

Find the equation of the line y = mx + c for:Gradient 2, y-intercept 5Gradient -1, passes through (0, 4)Passes …

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Parallel and perpendicular

Answer the following:Line A: y = 3x + 2. Give the gradient of a line parallel to A.Line B: y …

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