17.4 Loci — Practise
Work independently, then check your answers and reasoning.
- Describe the locus of points 6 cm from fixed point P.
- Describe the locus 2 cm from a straight line.
- What locus contains points equally distant from A and B?
- A point is 4 cm from a line measured perpendicularly. A sloping segment to the line is 5 cm. Can it be shorter?
- A point lies 3 cm above a horizontal line. State its perpendicular distance to the line.
- A point is 5 cm from P and equally distant from A and B. Which two loci must intersect?
- The water point is at the garden centre. What radius circle marks points 4 m away?
- A sloping segment and perpendicular segment both join a point to a line. Which is shorter?
Answers and concise solutions
1. Describe the locus of points 6 cm from fixed point P.
Answer: Circle centre P, radius 6 cm
2. Describe the locus 2 cm from a straight line.
Answer: Two parallel lines, 2 cm away on either side
3. What locus contains points equally distant from A and B?
Answer: Perpendicular bisector of AB
4. A point is 4 cm from a line measured perpendicularly. A sloping segment to the line is 5 cm. Can it be shorter?
Answer: No
5. A point lies 3 cm above a horizontal line. State its perpendicular distance to the line.
Answer: 3 cm
6. A point is 5 cm from P and equally distant from A and B. Which two loci must intersect?
Answer: Circle centre P radius 5 cm and perpendicular bisector of AB
7. The water point is at the garden centre. What radius circle marks points 4 m away?
Answer: Circle radius 4 m
8. A sloping segment and perpendicular segment both join a point to a line. Which is shorter?
Answer: The perpendicular segment