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A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2012 · Q56 Marks

The diagram shows a triangle ABC in which A has coordinates (1, 3), B has coordinates (5, 11) and angle ABC is 90°. The point X (4, 4) lies on AC. Find [Figure 5]

  1. (i)the equation of BC,[3]
  2. (ii)the coordinates of C.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [B1] Gradient of AB = 2
  2. [M1] Gradient of BC = -½ (using m₁m₂ = -1)
  3. [A1] Eqn of BC is y - 11 = -½(x - 5)
  4. [B1] gradient of AC (or AX) is ⅓
  5. [M1] Correct form of line equation + sim eqns (for AC using A or X)
  6. [A1] Sim equations → C(13, 7)

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About this question

Topic
Coordinate geometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2012 Paper 1 Variant 2, question 5.

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