Lemmara logoLemmaraWorked solution

4MA1/1FR Jun 2022, Question 7: Length of a Line Segment

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

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using points A, B and C marked on a centimetre grid, state A's coordinates, locate the midpoint of BC, calculate the area of triangle ABC, and mark point D so ABCD forms a rectangle.

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

Part (a) · 1 mark

Give the coordinates of point A as shown on the grid.

  1. 1Read the coordinates of point A from the grid: x = −1, y = 3
  2. 2(−1, 3)

Answer(−1, 3)

Part (b) · 2 marks

Determine the coordinates of the point halfway between B and C.

  1. 1B is the point (5, 3) and C is the point (5, −1).
  2. 2x-coordinate of the midpoint: (5 + 5) ÷ 2 = 5
  3. 3y-coordinate of the midpoint: (3 + (−1)) ÷ 2 = 1
  4. 4The midpoint of BC is (5, 1).

Answer(5, 1)

Part (c) · 2 marks

Calculate the area of the triangle formed by A, B and C.

  1. 1A(−1, 3), B(5, 3) and C(5, −1) make a right angle at B.
  2. 2Base AB = 5 − (−1) = 6 cm and height BC = 3 − (−1) = 4 cm
  3. 3Area = ½ × 6 × 4 = 12

Answer12

Part (d) · 1 mark

Place a cross at the grid point D that completes rectangle ABCD, and label it D.

  1. 1A is (−1, 3), B is (5, 3) and C is (5, −1).
  2. 2In rectangle ABCD, the step from A to D is the same as the step from B to C.
  3. 3From B(5, 3) to C(5, −1) is 0 across and 4 down.
  4. 4So D is 0 across and 4 down from A: D = (−1, 3 − 4) = (−1, −1)
  5. 5Mark a cross at (−1, −1) and label it D.

AnswerD indicated at (−1, −1)

Stuck on a step? Read the free lesson: Length of a Line Segment

Practise more length of a line segment questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on length of a line segment

Also searched as: 4MA1 1FR June 2022 · 4MA1/1FR · 4ma1 jun22 1fr · question 7.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.