4MA1/2H Jun 2023, Question 24: Coordinate Geometry of Shapes
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
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The question, in short
Kite ABCD has AB = AD and CB = CD, with A(−2, 10), B(−27/5, 4) and C(4, −5). Work out the coordinates of D.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1A and C are both equidistant from B and D, so AC is the perpendicular bisector of BD
- 2AC: gradient −15/6 = −2.5, so y = −2.5x + 5
- 3BD: gradient 0.4 through B(−5.4, 4), so y = 0.4x + 6.16
- 4They meet where 2.9x = −1.16: x = −0.4, y = 6 (midpoint of BD)
- 5D = (2 × −0.4 + 5.4, 2 × 6 − 4) = (4.6, 8)
Answer(4.6, 8)
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