17.4 Loci — Practise with help
Attempt each item before opening its help. Recall ideas from earlier chapters first.
Warm-up: remember
Answer these from memory. Do not look back at the section.
- What does a perpendicular bisector do to a line segment?
- What is the distance from the centre of a circle to any point on it called?
Check the warm-up
- It cuts the segment in half at a right angle.
- The radius.
If an answer differs, revisit Section 17.3 for the perpendicular bisector and for drawing circles with compasses.
Try these with help
1. Describe the locus of points 5 cm from point .
Hint
Use a fixed radius centred at .
Next step
A fixed distance from a point traces a circle.
Full answer
A circle centred at with radius 5 cm.
2. State the shortest distance from a point to a line.
Hint
Think about the angle made with the line.
Next step
The shortest segment meets the line at a right angle.
Full answer
The perpendicular distance, measured at .