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4024/12 May/Jun 2024, Question 10: Constructing Triangles

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Using a scale drawing of field ABCD at 1 cm to 50 m, find a bearing, complete the drawing from two distances, and construct a path.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Measure the bearing of C from B on the given drawing.

  1. 1Measure clockwise from the North line at B to the line BC
  2. 2Bearing of C from B ≈ 070° (068° to 072°)

Answer068 to 072

Part (b) · 2 marks

With D 250 m from C and 300 m from A, finish the scale drawing using ruler and compasses.

  1. 1250 m ÷ 50 = 5 cm and 300 m ÷ 50 = 6 cm
  2. 2Compasses 5 cm centred at C: draw an arc
  3. 3Compasses 6 cm centred at A: draw an arc crossing the first
  4. 4D is where the arcs cross; join CD and DA to complete ABCD

AnswerAcceptable quadrilateral with intersecting arcs

Part (c) · 2 marks

Construct the line of points equally far from AB and BC, using straight edge and compasses.

  1. 1The path equidistant from AB and BC is the bisector of angle ABC
  2. 2Arc centred at B cuts BA and BC; from these two points draw equal arcs that cross
  3. 3Rule the line from B through the crossing point (keep all arcs)

AnswerAcceptable angle bisector of ∠B with correct arcs

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