Loci Flashcards

All 7 cards in this deck

What is a locus?

The set of all points that satisfy a given rule or condition.

What is the locus of points a fixed distance from a single point?

A circle, centre that point, with radius equal to that distance.

What is the locus of points a fixed distance from a straight line segment?

Two parallel lines, one each side at that distance, joined by semicircles at the ends.

Which construction gives the locus of points equidistant from two points A and B?

The perpendicular bisector of AB.

Which construction gives the locus of points equidistant from two lines that meet?

The bisector of the angle between them.

What are the steps to shade a region satisfying two loci conditions?

e.g. inside a triangle, less than 4 cm from A and closer to C than to B

1. Draw the first locus: an arc of radius 4 cm, centre A
2. Draw the second locus: the perpendicular bisector of CB
3. Shade only the overlap: inside the arc and on C's side of the bisector

True or false? On a scale plan with scale $1:30$, "more than 180 cm from A" is drawn as an arc of radius 180 cm.

False. Convert first: $180 \div 30 = 6$ cm, so draw an arc of radius 6 cm and shade outside it.