EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Line Segments
Line segments · Graphs · Lesson 5 of 8 · 12 marks · 20 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [2 marks]
Find the midpoint of the line segment joining (−3, 5) and (7, 1).
Question 2 NON-CALCULATOR [4 marks]
A is the point (2, 3) and B is the point (8, 11). (a) Find the midpoint of AB. (b) Work out the length of AB.
Question 3 NON-CALCULATOR [2 marks]
M(3, 1) is the midpoint of the line segment AB. A has coordinates (−1, 4). Find the coordinates of B.
Question 4 NON-CALCULATOR · HIGHER [4 marks]
A is the point (1, 2) and B is the point (5, 10). Find an equation of the perpendicular bisector of AB.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
((−3 + 7)/2, (5 + 1)/2) = (2, 3)
▸ One coordinate correct B1
▸ (2, 3) B1
Question 2 [4 marks]
(a) (5, 7) (b) √(6² + 8²) = √100 = 10
▸ (a) (5, 7) B1
▸ (b) Differences 6 and 8 M1
▸ (b) 6² + 8² M1
▸ (b) 10 A1
Question 3 [2 marks]
B = (2 × 3 − (−1), 2 × 1 − 4) = (7, −2)
▸ One coordinate correct B1
▸ (7, −2) B1
Question 4 [4 marks]
Midpoint (3, 6). Gradient of AB = 2, so the perpendicular gradient is −½. 6 = −½ × 3 + c, c = 7.5. y = −½x + 7.5
▸ Midpoint (3, 6) P1
▸ Gradient of AB = 2 P1
▸ Perpendicular gradient −½ used with the midpoint P1
▸ y = −½x + 7.5, or x + 2y = 15 A1