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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

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?

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 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.

3. 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.

4. 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.

5. 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.

6. If a line segment AB is 10 cm long, how many points are simultaneously 6 cm from point A AND 6 cm from point B?

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

Circles of radius 6 cm centred at A and B intersect at 2 points (one above and one below segment AB, since 6 + 6 > 10).

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. 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.

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. 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.

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