Midpoints: Problem Solving & Reasoning
Mathematics
GCSE Foundation
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the concept of midpoints, helping GCSE Foundation students understand and apply midpoint calculations through a variety of problem types.
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Midpoints: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Read the key concept about midpoints below.
1.
The midpoint M of a line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂) is given by the coordinate formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
[2 marks]B
Fluency & Practice
Answer the following procedural questions on calculating midpoints.
1.
Find the midpoint of the segment with endpoints A(2, 4) and B(6, 8).
[2 marks]2.
Calculate the midpoint of the segment with A(0, -2) and B(4, 10).
[2 marks]3.
Determine the midpoint of the line segment with endpoints A(-3, 7) and B(3, -1).
[2 marks]C
Targeted Practice
Work through these questions to deepen your understanding of midpoints in coordinate geometry.
1.
Point M is the midpoint of segment AB. If A(1, 5) and M(4, 7), find the coordinates of B.
[3 marks]2.
The midpoint of segment CD is at (2, -3). If C(-4, 1), find the coordinates of D.
[3 marks]3.
The endpoints A and B of a segment are at (3, 2) and (7, 10). Find the midpoint.
[2 marks]D
Real-world Applications
Apply your knowledge of midpoints to these contextual problems.
1.
A drone starts at point A(0, 0) and flies to point B(8, 4). It then flies to point C, which is exactly halfway between A and B. What are the coordinates of C?
[3 marks]2.
A surveyor marks the midpoint of a land plot's diagonal. If one corner is at (10, 12) and the opposite corner at (22, 20), what is the midpoint?
[2 marks]E
Challenge & Extension
Tackle these advanced problems involving midpoints.
1.
Points A and B have coordinates A(2, -1) and B(10, 5). Find the coordinates of the midpoint. Then, find the gradient of the line AB and explain if the midpoint lies on the line between A and B.
[4 marks]2.
Construct a triangle with vertices at A(1, 2), B(5, 2), and C(3, 6). Find the midpoints of AB and AC, then determine if the midpoints are collinear.
[4 marks]F
Mixed Review
Solve a variety of questions to review midpoints.
1.
A segment has endpoints at (x₁, y₁) and (x₂, y₂). If the midpoint is at (x_m, y_m), express x₂ and y₂ in terms of x₁, y₁, x_m, and y_m.
[3 marks]2.
Identify the mistake in calculating the midpoint of A(4, 8) and B(10, 12) if a student finds it to be (7, 10). Correct the mistake.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet