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

A circle centered on the line

Answer

A single line parallel to the given line

Answer

A perpendicular bisector

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

Drawing the perpendicular bisector of the given line

Answer

Bisecting the angle between the point and the line

Answer

Constructing a circle at the given point

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

A circle centered between them

Answer

The perpendicular bisector of both lines

Answer

Two intersecting lines

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

Measure 60° at each endpoint and draw lines until they meet

Answer

Draw perpendicular bisector and measure up the same length

Answer

Bisect the segment and draw a vertical line

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

A straight line

Answer

An ellipse

Answer

A parabola

Question 6

How do you construct a perpendicular to a line through a point ON the line?

Accepted Answer

Draw two arcs from the point along the line, then bisect the resulting segment above the line

Answer

Measure 90° with a protractor at the point

Answer

Draw a circle at the point and find where it crosses the line

Answer

Copy the angle adjacent to the point