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:
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
c. Semicircle
b. Straight line
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
c. Rectangle
b. Straight line
d. Curve
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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
c. RP
b. QP
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
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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?
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