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4MA1/2FR Jan 2022, Question 2: Length of a Line Segment

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 5 marks

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The question, in short

From a grid diagram with points A, B and C, give coordinates of A and B, mark point D so ABCD is a rhombus, and find the midpoint of AB.

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

Part (ai) · 1 mark

State the coordinates of point A from the grid.

  1. 1Read the x-coordinate of point A as 3
  2. 2Read the y-coordinate of point A as 4
  3. 3Write coordinates as (3, 4)

Answer(3, 4)

Part (aii) · 1 mark

State the coordinates of point B from the grid.

  1. 1Read the x-coordinate of point B as −1
  2. 2Read the y-coordinate of point B as 2
  3. 3Write coordinates as (−1, 2)

Answer(−1, 2)

Part (b) · 1 mark

Mark point D on the grid so that ABCD forms a rhombus, labelling it D.

  1. 1In a rhombus the diagonals bisect each other, so AC and BD have the same midpoint
  2. 2From the grid A is (3, 4), B is (−1, 2) and C is (3, 0)
  3. 3Midpoint of AC = ((3 + 3) ÷ 2, (4 + 0) ÷ 2) = (3, 2)
  4. 4So the midpoint of BD is also (3, 2)
  5. 5Let D be (x, y): (−1 + x) ÷ 2 = 3 so x = 7
  6. 6(2 + y) ÷ 2 = 2 so y = 2
  7. 7Mark a cross at (7, 2) and label it D

Answer(7, 2)

Part (c) · 2 marks

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

  1. 1Find midpoint of AB
  2. 2x-coordinate: (3 + (−1)) / 2 = 2 / 2 = 1
  3. 3y-coordinate: (4 + 2) / 2 = 6 / 2 = 3
  4. 4Write coordinates as (1, 3)

Answer(1, 3)

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