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Worksheet Chapter 8: Loci in Two Dimensions

Form 3 Mathematics Bab 8: Loci in Two Dimensions

Instructions

Answer all questions based on Form 3 Chapter 8: Loci in Two Dimensions. Show clear constructions, reasoning steps, and descriptions where required.

10 questions · 22 marks total

1. Grid lines L1 and L2 are two parallel lines 10 cm apart. A fixed point P lies on L1. Point Z moves such that: Condition 1: It is equidistant from L1 and L2. Condition 2: It is 13 cm away from point P. Calculate the distance between the two possible intersection points satisfying both conditions.

Short Answer · 4m

2. Fill in the blank: The locus of a point equidistant from two intersecting lines is the ________ of the angle formed by the lines.

Fill in the Blank · 1m

3. True or False: The perpendicular bisector of line segment AB contains all points that are equidistant from point A and point B.

True / False · 1m

4. Construct/describe the locus of point X such that it is equidistant from two fixed points P and Q which are 6 cm apart. State the exact geometrical relationship between Locus X and line segment PQ.

Short Answer · 2m

5. Which of the following describes the locus of a point moving such that it is always 4 cm away from a straight line XY?

Multiple Choice · 1m
  1. A. A circle with radius 4 cm centred at the midpoint of XY
  2. B. A pair of parallel lines 4 cm away on either side of line XY
  3. C. The perpendicular bisector of XY
  4. D. A line perpendicular to XY at distance 4 cm

6. Two fixed points A and B are 8 cm apart. Point X moves such that AX = 5 cm, and point Y moves such that BX = 5 cm. (a) Describe Locus X and Locus Y. (b) Determine the number of intersection points between Locus X and Locus Y.

Short Answer · 3m

7. A rectangle ABCD has dimensions AB = 8 cm and BC = 6 cm. Describe the locus of a point P moving inside the rectangle such that it is always equidistant from line AB and line CD.

Short Answer · 2m

8. In a square ABCD with side length 6 cm: (a) State the locus of a point X that is equidistant from sides AB and AD. (b) State the locus of a point Y that is always 3 cm from vertex A. (c) Determine the number of intersection points between Locus X and Locus Y inside the square.

Short Answer · 3m

9. Triangle ABC is an isosceles triangle with AB = AC = 10 cm and BC = 12 cm. (a) Describe the locus of point P equidistant from vertex B and vertex C. (b) Calculate the distance from vertex A to the locus of P on line BC. (c) If point Q moves such that its distance from vertex A is constantly 8 cm, find the distance between the two points where Locus P intersects Locus Q.

Short Answer · 4m

10. True or False: The locus of a point at a constant distance from a fixed point in a 2D plane is a sphere.

True / False · 1m
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