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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. 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.

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. How many intersection points exist between a circle of radius 5 cm centred at O and a straight line passing directly through O?

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

A line passing through the centre of a circle intersects the circumference at two diametrically opposite points.

4. 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.

5. 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.

6. 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.

7. A car moves on a straight road. A streetlamp is located 10 m away from the road. What is the locus of points that are 10 m away from the streetlamp?

  1. A straight line parallel to the road
  2. A circle of radius 10 m centred at the streetlamp
  3. A line perpendicular to the road
  4. A point on the road
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Answer: B

The streetlamp is a fixed point, so points 10 m away form a circle of radius 10 m around it.

8. 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.

9. 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.

10. Point X moves such that it is always 3 cm from a fixed point O. Point Y moves such that it is always 3 cm from a straight line. Which statement correctly identifies Locus X?

  1. Locus X is a pair of parallel lines
  2. Locus X is a circle of radius 3 cm centred at O
  3. Locus X is a perpendicular bisector
  4. Locus X is an angle bisector
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Answer: B

A fixed distance from a single point O defines a circle with centre O and radius equal to that distance (3 cm).

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