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Quiz Chapter 8: Loci in Two Dimensions

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

Question 1 of 10Score: 0

The locus of a point that is equidistant from two fixed points P and Q is:

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1. The locus of a point that is equidistant from two fixed points P and Q is:

  1. A circle passing through P and Q
  2. The perpendicular bisector of the line segment PQ
  3. A line parallel to PQ
  4. The angle bisector of PQ
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Answer: B

Any point equidistant from two fixed points lies on the perpendicular bisector of the line segment joining them.

2. 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.

3. 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.

4. 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.

5. The locus of a point that is equidistant from two parallel lines L1 and L2 is:

  1. A parallel line halfway between L1 and L2
  2. A line perpendicular to L1 and L2
  3. A circle with diameter equal to the distance between L1 and L2
  4. Two intersecting lines
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Answer: A

The set of points equidistant from two parallel lines forms a single line parallel to both and located precisely midway between them.

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. Which of the following describes the locus of the tip of the minute hand of a wall clock as time passes?

  1. A straight vertical line
  2. A circle
  3. An angle bisector
  4. A pair of parallel lines
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Answer: B

The tip rotates at a constant distance (hand length) from the central pivot (fixed point), forming a circle.

8. 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.

9. What is the maximum number of intersection points between two non-identical circles in a plane?

  1. 1
  2. 2
  3. 3
  4. 4
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Answer: B

Two distinct circles can intersect at a maximum of 2 points.

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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