Geometry Geometry Constructions & Loci 2

Question 1

The locus of all points at a fixed distance from a given line is:

Accepted Answer

Two parallel lines, one on each side of the given line

Answer

All points equidistant from a line form two parallel lines, one on each side at that fixed distance.

Question 2

Which construction produces a line through a given point parallel to a given line?

Accepted Answer

Copying the angle formed by a transversal to create equal corresponding angles

Answer

By copying the angle a transversal makes with the given line at the new point, you create equal corresponding angles, producing a parallel line.

Question 3

What is the locus of all points equidistant from two parallel lines?

Accepted Answer

A third line parallel to and midway between them

Answer

The locus of points equidistant from two parallel lines is a single line parallel to both and midway between them.

Question 4

To construct an equilateral triangle on a given segment AB, you:

Accepted Answer

Set compass to length AB, draw arcs from A and B, connect intersection to A and B

Answer

Place the compass at A with radius AB and draw an arc, repeat from B; their intersection is the third vertex, and all sides will equal AB.

Question 5

What is the locus of the vertex of a right angle whose two sides pass through two fixed points?

Accepted Answer

A circle with the two fixed points as endpoints of a diameter

Answer

By Thales' theorem, any angle inscribed in a semicircle is a right angle, so the locus is a circle with the two points as diameter endpoints.

Geometry Practice Test