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4MA1/1FR Jun 2024, Question 9: Length of a Line Segment

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks

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The question, in short

From a grid diagram with points A, B and C, write down A's coordinates, find the midpoint of AB, and determine D so that ABCD is a rectangle.

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

Part (a) · 1 mark

State the coordinates of point A as marked on the grid.

  1. 1Point A is located at the grid position where x = −4 and y = 2.
  2. 2Therefore, coordinates of A are (−4, 2).

Answer(−4, 2)

Part (b) · 2 marks

Calculate the coordinates of the midpoint of the line segment AB.

  1. 1Coordinates of A: (−4, 2)
  2. 2Coordinates of B: (2, 4)
  3. 3Midpoint x-coordinate: (−4 + 2) / 2 = −2 / 2 = −1
  4. 4Midpoint y-coordinate: (2 + 4) / 2 = 6 / 2 = 3
  5. 5Therefore, midpoint of AB is (−1, 3).

Answer(−1, 3)

Part (c) · 2 marks

Find the coordinates of point D that makes ABCD a rectangle.

  1. 1A(−4, 2), B(2, 4), C(3, 1)
  2. 2Vector BC = (3 − 2, 1 − 4) = (1, −3)
  3. 3In rectangle ABCD, vector AD = vector BC
  4. 4So D = A + (1, −3) = (−4 + 1, 2 − 3) = (−3, −1)
  5. 5Therefore, coordinates of D are (−3, −1).

Answer(−3, −1)

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