EDEXCEL GCSE FOUNDATION MATHS - What is Loci

Edexcel GCSE Foundation Maths: What are Loci?

What is a Locus?

A locus is a set of points that satisfy a specific condition. Imagine you have a rule, and you need to find all the points that follow that rule. These points, when plotted, will form a shape or a path – that's your locus!

Examples:

• Points equidistant from a point: Imagine a point 'A' in the centre of a circle. All points on the circle are the same distance from point 'A'. This distance is the radius of the circle. Therefore, the locus of points equidistant from a point is a circle.
• Points equidistant from a line: Imagine a line segment. All points that are the same distance away from the line segment form a pair of parallel lines, one on each side of the line segment.
• Points a fixed distance from a line: Imagine a line segment and you need to find all points that are 2cm away from the line segment. You would draw lines parallel to the line segment, each 2cm away, creating two parallel lines.

Constructing Loci:

1. Understand the Condition: Read the problem carefully and identify the rule that defines the locus.
2. Choose a Tool: You will need a compass, ruler, or protractor to help you draw the locus.
3. Start Plotting: Start by plotting a few points that satisfy the condition.
4. Connect the Points: Connect the plotted points to form the shape or path of the locus.

Common Loci:

• Circle: All points equidistant from a fixed point.
• Straight Line: All points equidistant from two fixed points.
• Perpendicular Bisector: All points equidistant from two fixed points.
• Angle Bisector: All points equidistant from the arms of an angle.

Applications of Loci:

• Navigation: Ships and airplanes use loci to navigate and avoid obstacles.
• Architecture: Architects use loci to design buildings and structures.
• Engineering: Engineers use loci to design bridges and other structures.

Practice:

Practice constructing loci by following the examples and trying different scenarios. Remember to understand the condition, choose the right tool, and carefully plot the points.

Key takeaways:

• A locus is a set of points that satisfy a specific condition.
• Common loci include circles, straight lines, perpendicular bisectors, and angle bisectors.
• Loci have applications in various fields, including navigation, architecture, and engineering.