Online Test — Loci
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
What geometric shape is formed by the locus of a point moving at a fixed distance from a single fixed point?
Straight Line
Square
Circle
Triangle
Explanation: By definition, a point keeping a constant distance from a center traces a circle.
Question 2 of 10
medium
The locus of a point equidistant from two fixed points is geometrically called a...
Tangent Line
Perpendicular Bisector
Angle Bisector
Median
Explanation: The perpendicular bisector is the unique path that splits the distance between two points evenly at 90 degrees.
Question 3 of 10
medium
How many lines make up the complete locus of a point equidistant from two intersecting lines?
One Line
Two Lines
Four Lines
Infinite Lines
Explanation: It consists of two perpendicular lines that bisect both the acute and obtuse angle pairs.
Question 4 of 10
medium
A point P moves such that it is always 4 cm away from a fixed point O. What is the diameter of the path traced by P?
4 cm
2 cm
8 cm
16 cm
Explanation: The fixed distance is the radius (4 cm), so the full diameter is 2 * 4 = 8 cm.
Question 5 of 10
medium
If a point lies on the perpendicular bisector of segment AB, its distance from point A is always...
Greater than to B
Less than to B
Equal to its distance from B
Double its distance from B
Explanation: "Equidistant" means the distance to endpoint A matches the distance to endpoint B exactly.
Question 6 of 10
medium
If the angle between two intersecting lines is 80 degrees, what is the angle between one of the lines and its nearest angle bisector?
40 degrees
20 degrees
80 degrees
45 degrees
Explanation: An angle bisector cuts the opening angle exactly in half: 80 / 2 = 40 degrees.
Question 7 of 10
medium
What is the angle formed between the two locus lines that bisect a pair of intersecting lines?
45 degrees
60 degrees
90 degrees
180 degrees
Explanation: The internal and external angle bisectors of intersecting lines are always perpendicular.
Question 8 of 10
medium
A moving point stays equidistant from two parallel lines. What is its resulting locus?
A circle
A line parallel to both, running halfway between them
A perpendicular line
A single point
Explanation: The path is a third parallel line running down the exact center of the channel.
Question 9 of 10
medium
The point of intersection of the three perpendicular bisectors of a triangle's sides is called the...
Centroid
Incenter
Orthocenter
Circumcenter
Explanation: The circumcenter is equidistant from all three vertices because it is the intersection of the perpendicular bisectors.
Question 10 of 10
medium
The locus of a point equidistant from the three boundary sides of a triangle is found by locating the intersection of its...
Medians
Altitudes
Angle Bisectors
Perpendicular Bisectors
Explanation: Angle bisectors generate points equidistant from the sides, meeting at the triangle's incenter.