Lesson 11: Practice and Revision

Overview

Use these mixed practice sets to consolidate learning across all coordinate geometry topics. These can be used for in-class revision or homework.

Practice Set A: Coordinates and Quadrants

  1. State the quadrant or axis for each point:
    • A(3, -5)
    • B(-4, 2)
    • C(0, -7)
    • D(6, 0)
    • E(-2, -3)

Practice Set B: Distance and Midpoint

  1. Find the distance between (-1, 4) and (5, 1).
  2. Find the midpoint of (-6, 2) and (4, -4).
  3. Find the distance from the origin to (7, -24).

Practice Set C: Gradients and Line Equations

  1. Find the gradient of the line through (-2, 1) and (4, 7).
  2. Write the equation of the line with gradient -3 passing through (2, -1).
  3. Find the equation of the line through (0, -2) and (3, 4).
  4. Convert \(4x - 2y + 6 = 0\) to slope-intercept form.

Practice Set D: Parallel and Perpendicular Lines

  1. Determine whether each pair of lines is parallel, perpendicular, or neither:
    • \(y = -2x + 1\) and \(y = -2x - 4\)
    • \(y = \frac{1}{4}x + 3\) and \(y = -4x + 2\)
  2. Find the equation of:
    • The line perpendicular to \(y = \frac{1}{2}x - 5\) through (0, 2)
    • The line parallel to \(3x + y - 9 = 0\) through (1, -1)

Set A: A QIV, B QII, C y-axis, D x-axis, E QIII

Set B: \(3\sqrt{5}\), (-1, -1), 25

Set C: \(m = 1\), \(y = -3x + 5\), \(y = 2x - 2\), \(y = 2x + 3\)

Set D: Parallel, perpendicular, \(y = -2x + 2\), \(y = -3x + 2\)

Previous Lesson: Lesson 10: Equation of a Line from Gradient and a Point
Next Lesson: Answer Key Appendix