Answer Key Appendix

Lesson 1: Introduction to Cartesian Coordinates

Practice Exercises (sample answers)

  1. Plot as given.
  2. A QI, B QII, C QIII, D QIV, E y-axis, F x-axis.
  3. G(2, 6) QI; H(-5, 4) QII; I(0, -3) y-axis; J(-7, 0) x-axis; K(-2, -5) QIII.
  4. Any valid points.
  5. Any valid set, one in each quadrant.

Exit Ticket (sample answers)

  1. Plot as given.
  2. A QIV, B QIII, C y-axis.
  3. Example: (-2, -4) in QIII and (0, 5) on y-axis.

Worksheet 1A

A QI, B QII, C QIII, D QIV, E y-axis.

Lesson 3: The Distance Formula

Worksheet 1B

  1. AB = 5
  2. CD = 13
  3. EF = 13

Lesson 4: The Midpoint Formula

Worksheet 1C

  1. (6, 6)
  2. (1, 3)

Lesson 5: Gradient Basics (Rise/Run)

Practice Answers

  1. \(\frac{2}{5}\), \(-2\), \(0\)
  2. Negative, zero, undefined
  3. 4

Lesson 6: Gradient Using the Formula

Practice Answers

  1. \(2\), \(-1\), \(0\)
  2. Undefined, zero
  3. Example: (0, 4) or (4, -2)

Lesson 7: Linear Equations and Intersections

Worksheet 2B

  1. \(y = 3x + 5\), \(y = -2x + 9\), \(y = 2x - 1\)
  2. \(y = -\frac{1}{2}x + 5\), \(y = 2x + 3\)
  3. (3, 5), (4, 0)

Lesson 8: Parallel Lines

Worksheet 3A

  1. Parallel, not parallel
  2. \(y = 5x - 7\), \(y = -2x + 3\)

Lesson 9: Perpendicular Lines

Worksheet 3B

  1. Perpendicular, not perpendicular
  2. \(y = \frac{1}{3}x + 2\), \(y = -\frac{1}{5}x + \frac{13}{5}\)
  3. \(y = -x + 9\), \(m = -2\)

Lesson 10: Equation of a Line from Gradient and a Point

Worksheet 2C

  1. \(y = 2x - 5\), \(y = -\frac{1}{2}x + 7\)
  2. \(y = 5x + 12\), \(y = -3x + 10\)
  3. Yes, yes

Lesson 11: Practice and Revision

Answer Key

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, \(y = -2x + 2\), \(y = -3x + 2\)

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