Constructions and Loci Quiz

1. When constructing a perpendicular bisector of a line segment using a compass and ruler, what is the key property that ensures the construction is accurate?

• A. All points on the perpendicular bisector are equidistant from the two endpoints of the line segment
• B. The perpendicular bisector passes through the midpoint at a 45° angle
• C. The compass arc radius must be exactly half the length of the line segment
• D. The perpendicular bisector divides the line segment into two equal angles

2. Which of the following standard angles can be constructed using only a compass and ruler by first constructing a 60° angle?

• A. 30° only
• B. 30° and 120°
• C. 30°, 120° and 15°
• D. 45° and 90° only

3. A point P lies on the locus of points equidistant from two intersecting lines. What does this locus represent?

• A. A perpendicular line between the two lines
• B. The angle bisectors of the two lines
• C. A circle centred at the intersection point
• D. A single straight line parallel to both lines

4. To construct a perpendicular from a point P to a line AB using compass and ruler, which property is used?

• A. The perpendicular is always the shortest distance from the point to the line
• B. The perpendicular meets the line at a 90° angle, which is found using the perpendicular bisector method
• C. The distance from P to any point on the perpendicular is constant
• D. The perpendicular creates two equal angles with the line

5. A region is defined by the combined conditions: points closer to line L than 3 cm, and also closer to point Q than to point R. Which constructions must be used to accurately identify this region?

• A. Only parallel lines 3 cm from L, and the perpendicular bisector of QR
• B. A perpendicular from Q to L, and an angle bisector
• C. Parallel lines 3 cm from L, and the perpendicular bisector of QR
• D. Two circles of radius 3 cm, and a perpendicular line through Q