Applying constructions to loci problems | Maths | Quizalize & Oak National Academy

Starter quiz

A __________ is a set of points that satisfy a given set of conditions.

arc

circle

line

locus ✓

ray
Which diagram shows the locus of points 3 metres or less from point A?

Diagram a

Diagram b

Diagram c ✓

Diagram d
Which diagram shows the locus of points more than 3 metres from point A?

Diagram a

Diagram b ✓

Diagram c

Diagram d
Which diagram shows the locus of points 6 cm from the line segment AB?

Diagram a

Diagram b

Diagram c ✓

Diagram d
Which diagram shows the locus of points less than 6 cm from the line segment AB?

Diagram a

Diagram b

Diagram c

Diagram d ✓
Alex stands somewhere in his garden. Alex is less than 5 m from the house and more than 6 m from the tap. He is within 3 m of the tree. Alex is standing in region ______.

'E' ✓

Which diagram shows a perpendicular bisector?
Alex places two cones, A and B, on the ground. Which of these points are equidistant from A and B?

a

c ✓

f

g ✓

h
Which of these points are closer to TU than they are to ST?

b

c

e ✓

g ✓

f
Jacob wants to find all the points that are the same distance from LM as they are from MN. What construction should he use?

The arc of a circle centred on M.

The perpendicular bisector of LM

The perpendicular bisector of MN

The perpendicular bisectors of MN and LM

The angle bisector of ∠LMN ✓
Which region is illustrated on this diagram?

The region of points that are closer to A than to B.

The region of points that are closer to B than to A.

The region of points that are equidistant from A and B or closer to A than to B. ✓

The region of points that are equidistant from A and B or closer to B than to B.
Select the region which matches this description: closer to AB than BC and closer to CD than AD .

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The perpendicular bisector of a line segment divides the line segment into two equal parts
The perpendicular bisector is the same distance from each end point of the line segment
If you only had the two end points, the perpendicular bisector would still be the same distance from each point
The bisector of an angle divides the angle into two equal parts.

Pupils may believe that there is only one point which is equidistant from two points.

Highlight that forming any isosceles triangle will mean that that the point is equidistant from both points.

Bisect - To bisect means to cut or divide an object into two equal parts.
Loci - A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.
Equidistant - Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.