AI generatedGeometry and measuresKS3 / GCSE

Locus a fixed distance from a point

Locus a fixed distance from a point.

  • A locus is the set of all points satisfying a distance rule.
  • Distance to a straight line is always measured perpendicularly.
  • For two conditions, keep only the region satisfying both.

Example 1

Draw the locus of points exactly 3 cm from P.

Construction: given informationP
A circle centred on P with radius 3 cm.
Construction: given informationP3 cm

Every point on the circumference is the same distance from P. The interior is not included when the distance is exactly specified.

Example 2

Draw the locus of points exactly 4 cm from P.

Construction: given informationP
A circle centred on P with radius 4 cm.
Construction: given informationP4 cm

Every point on the circumference is the same distance from P. The interior is not included when the distance is exactly specified.

Your turn

Question 1

Draw the locus of points exactly 5 cm from P.

Construction: given informationP
Check answer
A circle centred on P with radius 5 cm.
Construction: given informationP5 cm

Every point on the circumference is the same distance from P. The interior is not included when the distance is exactly specified.

Question 2

Draw the locus of points exactly 6 cm from P.

Construction: given informationP
Check answer
A circle centred on P with radius 6 cm.
Construction: given informationP6 cm

Every point on the circumference is the same distance from P. The interior is not included when the distance is exactly specified.

Question 3

Draw the locus of points exactly 7 cm from P.

Construction: given informationP
Check answer
A circle centred on P with radius 7 cm.
Construction: given informationP7 cm

Every point on the circumference is the same distance from P. The interior is not included when the distance is exactly specified.

Question 4

Draw the locus of points exactly 8 cm from P.

Construction: given informationP
Check answer
A circle centred on P with radius 8 cm.
Construction: given informationP8 cm

Every point on the circumference is the same distance from P. The interior is not included when the distance is exactly specified.

Question 5

Draw the locus of points exactly 9 cm from P.

Construction: given informationP
Check answer
A circle centred on P with radius 9 cm.
Construction: given informationP9 cm

Every point on the circumference is the same distance from P. The interior is not included when the distance is exactly specified.