AI generatedGeometry and measuresKS3 / GCSE

Combining loci to find region

Combining loci to find region.

  • 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

AB = 15 cm. Shade points within 9 cm of A and closer to B than to A.

Construction: given informationAB
Shade the part of the circle on the B side of the perpendicular bisector.
Construction: given informationABAB = 15 cmradius 9 cm

Draw the circle about A. Bisect . The required region satisfies both conditions. The dashed bisector itself is excluded by “closer”.

Example 2

AB = 20 cm. Shade points within 12 cm of A and closer to B than to A.

Construction: given informationAB
Shade the part of the circle on the B side of the perpendicular bisector.
Construction: given informationABAB = 20 cmradius 12 cm

Draw the circle about A. Bisect . The required region satisfies both conditions. The dashed bisector itself is excluded by “closer”.

Your turn

Question 1

AB = 25 cm. Shade points within 15 cm of A and closer to B than to A.

Construction: given informationAB
Check answer
Shade the part of the circle on the B side of the perpendicular bisector.
Construction: given informationABAB = 25 cmradius 15 cm

Draw the circle about A. Bisect . The required region satisfies both conditions. The dashed bisector itself is excluded by “closer”.

Question 2

AB = 30 cm. Shade points within 18 cm of A and closer to B than to A.

Construction: given informationAB
Check answer
Shade the part of the circle on the B side of the perpendicular bisector.
Construction: given informationABAB = 30 cmradius 18 cm

Draw the circle about A. Bisect . The required region satisfies both conditions. The dashed bisector itself is excluded by “closer”.

Question 3

AB = 35 cm. Shade points within 21 cm of A and closer to B than to A.

Construction: given informationAB
Check answer
Shade the part of the circle on the B side of the perpendicular bisector.
Construction: given informationABAB = 35 cmradius 21 cm

Draw the circle about A. Bisect . The required region satisfies both conditions. The dashed bisector itself is excluded by “closer”.

Question 4

AB = 40 cm. Shade points within 24 cm of A and closer to B than to A.

Construction: given informationAB
Check answer
Shade the part of the circle on the B side of the perpendicular bisector.
Construction: given informationABAB = 40 cmradius 24 cm

Draw the circle about A. Bisect . The required region satisfies both conditions. The dashed bisector itself is excluded by “closer”.

Question 5

AB = 45 cm. Shade points within 27 cm of A and closer to B than to A.

Construction: given informationAB
Check answer
Shade the part of the circle on the B side of the perpendicular bisector.
Construction: given informationABAB = 45 cmradius 27 cm

Draw the circle about A. Bisect . The required region satisfies both conditions. The dashed bisector itself is excluded by “closer”.

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