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4MA1/2H Jan 2021, Question 18: Coordinate Geometry of Shapes

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

Rectangle ABCD on a centimetre grid with A(−4, −2) and B(1, 10); find the missing coordinates of C and D, then the rectangle's perimeter in centimetres.

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

Part (a) · 4 marks

Given A(−4, −2) and B(1, 10), work out the values of a, b and c in C(19, a) and D(b, c).

  1. 1Gradient AB = (10 − (−2)) ÷ (1 − (−4)) = 12/5
  2. 2BC is perpendicular to AB, so gradient BC = −5/12
  3. 3(a − 10) ÷ (19 − 1) = −5/12, so a − 10 = −7.5 and a = 2.5
  4. 4D = A + (C − B): b = −4 + 18 = 14, c = −2 − 7.5 = −9.5
  5. 5a = 2.5, b = 14, c = −9.5

Answera = 2.5, b = 14, c = −9.5

Part (b) · 3 marks

Using A(−4, −2), B(1, 10), C(19, 2.5) and D(14, −9.5), calculate the perimeter of rectangle ABCD in centimetres.

  1. 1AB = √((1 − (−4))² + (10 − (−2))²)
  2. 2AB = √(5² + 12²) = √(25 + 144) = √169 = 13
  3. 3BC = √((19 − 1)² + (2.5 − 10)²)
  4. 4BC = √(18² + (−7.5)²) = √(324 + 56.25) = √380.25 = 19.5
  5. 5Perimeter = 2 × (AB + BC) = 2 × (13 + 19.5)
  6. 6Perimeter = 2 × 32.5 = 65

Answer65

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