Mastering Constructions & Loci
Mathematics
GCSE Foundation
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A worksheet covering Constructions & Loci for GCSE Foundation students.
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Mastering Constructions & Loci
Subject: MathematicsGrade: GCSE Foundation
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Date:
Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Review the key constructions and the concept of loci. Remember, a locus is a set of points satisfying a specific condition.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Construct an equilateral triangle with side length 6 cm. Label the vertices.
[2 marks]2.
Draw the bisector of the angle at point A in triangle ABC. Show all steps clearly.
[3 marks]3.
Using a compass, draw a circle centered at point P with radius 4 cm. Mark any point Q on the circle.
[2 marks]4.
Construct a perpendicular bisector of line segment AB. Label the point of intersection.
[3 marks]5.
Construct a rectangle with length 8 cm and width 3 cm. Label all vertices.
[2 marks]6.
Draw and label the locus of points equidistant from points X and Y.
[4 marks]7.
A point P moves so that it remains 5 cm from point Q. Describe the locus of P.
[4 marks]8.
Given a triangle with vertices A, B, and C, construct the locus of points equidistant from A and B, and verify with a diagram.
[4 marks]9.
In a circle, construct the locus of points that are 3 cm from the circumference. What shape do these points form?
[4 marks]10.
Challenge: A farmer wants to place a water tank so that it is equally accessible from two sheds 12 m apart. Construct the locus of possible locations for the tank.
[5 marks]11.
Real-world application: A drone must fly around a restricted zone represented by a circle of radius 5 km. Draw the possible flight paths for the drone if it must stay exactly 5 km from the zone boundary.
[5 marks]Quick Actions
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- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet