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Quiz Chapter 8: Loci in Two Dimensions

10 questions · Form 3 Mathematics Bab 8: Loci in Two Dimensions

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Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. A point P moves such that it is equidistant from vertices B and C of an equilateral triangle ABC. Which line segment represents the locus of P?

  1. Side BC
  2. The perpendicular bisector of side BC (passing through vertex A)
  3. The angle bisector of angle B
  4. A line parallel to AB
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Answer: B

The locus equidistant from two points B and C is the perpendicular bisector of segment BC, which passes through vertex A in an equilateral triangle.

2. What is the definition of a locus in 2D space?

  1. A 3D projection of a moving line
  2. A path or set of points that satisfies specific geometric conditions
  3. An angle formed by two intersecting arcs
  4. A line that divides a shape into two equal parts
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Answer: B

A locus is a set of points or a path traced out by a moving point that satisfies one or more given rules.

3. If Locus 1 is a circle of radius 4 cm centred at (0,0) and Locus 2 is a circle of radius 2 cm centred at (0,0), how many points of intersection exist between Locus 1 and Locus 2?

  1. 0
  2. 1
  3. 2
  4. 4
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Answer: A

Concentric circles of different radii never touch or cross, so there are 0 points of intersection.

4. A goat is tied to a stake in an open field with a 4-metre rope. What is the locus of the maximum area the goat can reach?

  1. A square of side 4 m
  2. A circle of radius 4 m centred at the stake
  3. A line of length 8 m
  4. A semicircle of radius 2 m
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Answer: B

Tied to a fixed stake (fixed point) with a 4 m rope, the boundary of the movement is a circle of radius 4 m.

5. What is the locus of a point moving at a fixed distance d from a straight line AB?

  1. A circle of radius d
  2. A single perpendicular line
  3. A pair of parallel lines at distance d on either side of AB
  4. The midpoint of line AB
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Answer: C

Points at a constant distance from a straight line form two parallel lines running on both sides of the line.

6. Point M is 5 cm away from line L. How many points on line L are at a distance of 8 cm from point M?

  1. 0
  2. 1
  3. 2
  4. Infinitely many
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Answer: C

Since the distance from M to line L (5 cm) is less than 8 cm, a circle of radius 8 cm centred at M intersects line L at 2 points.

7. Two parallel lines are 6 cm apart. What is the distance from either parallel line to the locus of points equidistant from both lines?

  1. 6 cm
  2. 3 cm
  3. 12 cm
  4. 1.5 cm
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Answer: B

The locus lies midway between the two parallel lines, so its distance from either line is 62 = 3 cm.

8. In a rectangle PQRS, what is the locus of a point moving equidistant from line PQ and line SR?

  1. Diagonal PR
  2. A line parallel to PQ and SR passing through the midpoints of PS and QR
  3. The perpendicular bisector of PQ
  4. A circle centred at the intersection of diagonals
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Answer: B

PQ and SR are parallel lines. The locus equidistant from two parallel lines is a parallel line halfway between them.

9. If a point moves inside a square ABCD such that it is always equidistant from side AB and side AD, what is its locus?

  1. The diagonal AC
  2. The perpendicular bisector of BD
  3. The midpoint of side BC
  4. A circle inside the square
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Answer: A

Sides AB and AD intersect at vertex A. The locus equidistant from two intersecting sides is the angle bisector of angle DAB, which is diagonal AC.

10. What geometric path is formed by a point moving equidistant from two intersecting lines?

  1. Perpendicular bisector
  2. Angle bisector
  3. Circle
  4. Parallel line
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Answer: B

Points equidistant from two intersecting lines lie on the angle bisector of the angle formed between those lines.

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