Chapter 17: Properties, constructions, loci and bearings

The chapter problem: plan a safe route

A community garden is a rectangular site, $24$ m east to west and $18$ m north to south. A water point lies at the centre. A straight path runs from the south-west corner to the north-east corner. A circular planting bed has its centre at the water point and radius $4$ m.

First contact: predict whether the path is longer or shorter than $30$ m. Estimate the path's bearing from the south-west corner. No exact answer is needed yet.

At the end, you will draw the plan to scale, describe the path using a bearing, construct the centre lines, and show where points exactly $4$ m from the water point can lie.

By the end of this chapter you will be able to

• name and use the parts, properties and symmetries of 2D and 3D shapes;
• read and draw plans and elevations of 3D shapes;
• use a ruler and compasses to construct perpendiculars and bisect angles;
• describe and solve problems about loci, including shortest distance to a line;
• measure angles and lengths, read scale drawings, and use three-figure bearings.

Roadmap

1. 17.1 Properties of 2D and 3D shapes
2. 17.2 Plans and elevations
3. 17.3 Constructions with ruler and compasses
4. 17.4 Loci
5. 17.5 Bearings and scale drawings
6. Review

Your turn to connect it

Where might you or someone you know use a plan, a direction, or a measured boundary? Write one example. At the end, add how one idea from this chapter could help.