Loci in Two Dimensions

LOCI IN TWO DIMENSIONS

1. A locus in two dimensions is the PATH along which A POINT MOVES

in a plane so as to satisfy some given conditions.

2. For examples:

1

2

3. Describing the situations of 4 basic loci:

a. Situation 1: A point P moves in such a way that it is always x

cm from a fixed point.

Locus: A circle

Example: The chairs on Ferris wheel rotates in a clockwise

direction.

3

b. Situation 2 : A point Q moves so that it is equidistant from two

fixed points, A and B.

Locus : A perpendicular bisector

Example : The captain of a ship ensures that the ship is always

equidistant from two island to avoid any accident.

4

4. Situation 3: A point X moves so that it is always 5cm from a straight

line PQ.

Locus: Two parallel lines

Example: A boy running parallel to a fence.

5

5. Situation 4: A point P moves so that it is always equidistant fro two

intersecting lines L1 and L2.

Locus: Angle bisector

Example: A lizard crawls on the ceiling so that it is equidistant from

two adjoining walls.

6

Example 1:

Sketch and state the locus of the girl playing on the swing.

Example 2:

Sketch and state the locus of the feet of the boy riding a bicycle.

Example 3:

Sketch and state the locus of the crab.

7

Example 4:

TUVW is a square. Construct the locus of a moving point which is always

equidistant from TU and TW.

Example 5:

A point moves so that it is always 4 cm from a straight line MN. Construct the

locus of the point below.

Example 6:

Sketch and state the locus of an oscillation of a pendulum bob.

8

Example 7:

Sketch and state the locus of an ant that crawls in such a way that it always

equidistant from two flower pots, A and B

Example 8:

Sketch and state the locus of the tip of a moving helicopter’s rotor fan.

Example 9:

Sketch and state the locus of the boy playing on the slide.

9

6. The intersection of two loci on a two-dimensional plane is

a point / points which satisfy the conditions of both loci.

7. The intersection may be determined by constructing the two loci on

the same diagram.

Example:

The diagram below shows a rhombus of sides 13cm. PTR and QTS are

straight lines and TR=5cm. Which among the points A, B, C and D is

equidistant from PQ and QR but less than 12cm from Q?

Solution:

In the rhombus PQRS, QR-13 and TR=5cm. Therefore, QT=12cm

(Pythagoras Theorem)

Both A and C are equidistant from PQ and QR but only A is less than

12cm from Q. So, answer is A.

10

Unit title LOCI IN TWO DIMENSION – CD ( _____________ )

Teacher(s) MR. SHAHRUL

Subject and grade level MATHEMATICS MYP 3

Time frame and duration

1. The locus of a basketball when thrown is a

a. Circle

b. Straight line

c. Semicircle

d. Curve

2. Which of the following shows the locus of an arrow which is released

horizontally?

3. The locus of a point moving in such a way that it is always 3cm from a

fixed point O is a

a. Circle

b. Straight line

c. Rectangle

d. Curve

11

4. The diagram below shows a straight line KL. P is a point which moves

so that it is equidistant from K and L. which of the following is the locus

of P?

5. The diagram below shows a kite PQRS. The locus of a point, within the

kite, which moves so that it is equidistant from the point Q and the

point S is

a. RQ

b. QP

c. RP

d. RS

6. The above diagram shows a disc with centre O. When the disc is

rotated through 360°, the locus of the point P is a

a. Straight line PR

b. Rectangle PQRS

c. Semicircle

d. Full circle

12

7. A point M moves so that it is always 4cm from a fixed point O. Which of

the following is the locus of point M?

13