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A-LevelMathematicsCoordinate geometry9709/12 · May/June 2012 · Q46 Marks

The point A has coordinates (−1, −5) and the point B has coordinates (7, 1). The perpendicular bisector of AB meets the x-axis at C and the y-axis at D. Calculate the length of CD.

  1. The point A has coordinates (−1, −5) and the point B has coordinates (7, 1). The perpendicular bisector of AB meets the x-axis at C and the y-axis at D. Calculate the length of CD.[6]

Mark scheme

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

  1. [B1] Midpoint M = (3, -2); co
  2. [B1] Gradient of AB = (1 - (-5)) / (7 - (-1)) = 6/8 = 3/4; co
  3. [B1] Perpendicular gradient = -4/3; needs to be perp. through M.
  4. [M1] Equation of the perpendicular bisector: y - (-2) = -4/3 (x - 3); Correct method.
  5. [M1] To find C, set y=0. To find D, set x=0. C(3/2, 0) and D(0, 2); Sets x and y to 0.
  6. [M1A1] Length CD = √((3/2 - 0)² + (0 - 2)²) = √(9/4 + 4) = √(25/4) = 2.5; Pythagoras and final answer co.

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About this question

Topic
Coordinate geometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2012 Paper 1 Variant 2, question 4.

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