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4MA1/1H Jan 2020, Question 22: Coordinate Geometry of Shapes

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks

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The question, in short

Isosceles triangle HJK has HJ = HK, JK = √80, H(−4, 1), J(j, 15) with j < 0, K(6, k), and midpoint M of JK with gradient HM = 2. Find j and k.

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

Solution · 6 marks

  1. 1HJ = HK, so HM is perpendicular to JK: gradient of JK = −1/2
  2. 2(k − 15)/(6 − j) = −1/2, so 2k − j = 24
  3. 3M = ((j + 6)/2, (k + 15)/2); gradient HM = (k + 13)/(j + 14) = 2, so k = 2j + 15
  4. 4Substitute: 2(2j + 15) − j = 24, so 3j = −6 and j = −2
  5. 5k = 2(−2) + 15 = 11, so j = −2, k = 11

Answerj = −2, k = 11

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