4MA1/2H Jun 2022, Question 22: 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
On a 1 cm grid, kite ABCD has A(−3, 4), diagonals meeting at M(0, 2), AB = AD = 6.5 cm, and B's x-coordinate positive; find coordinates of B and D.
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Solution · 7 marks
- 1Gradient of AM = (4 − 2) ÷ (−3 − 0) = −2/3
- 2BD is perpendicular to AC, so its gradient is 3/2 and BD: y = 1.5x + 2
- 3AB = 6.5: (x + 3)² + (1.5x + 2 − 4)² = 42.25
- 4Expand: 3.25x² + 13 = 42.25, so x² = 9 and x = 3 or −3
- 5x = 3 gives y = 6.5; x = −3 gives y = −2.5
- 6B (3, 6.5) and D (−3, −2.5)
AnswerB = (3, 6.5), D = (−3, −2.5)
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