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Locus is the path of a moving point or a point or set ofpoints that satisfies given conditions.

A figure of 8 A circle

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circle

vertical line pentagon

square triangle

curve / arc

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Describe and sketch the locus of the moving point

The tip of a minute hand rotating on the face of aclock.A circle

A stone is dropped from the first floor of a building.A vertical line

The Earth revolves round the sun.An ellipse / a oval circle

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A swinging pendulum.

An arc

The centre of the wheel of a moving vehicleon the road.

A horizontal straight line

A competitor running in a 400 m race in the

field.An oval

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Exercise:

9.1A Question 2

9.1B All

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The locus of a moving point Pthat is at a constant distancefrom a fixed point Ois a circle with centre O.

O

P

Locus of P

The locus of Pis a circle withradius OPand centre O.

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The locus of a moving point Requidistantfrom two fixedpoints Aand Bis the perpendicular bisector of the lineAB

.

|| ||

The locus of Ris the perpendicular bisector of AB.

A B

Locus of R

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The locus of a moving point that is a constant distance froma straight line ABare two straight lines that are parallel to

AB.

A B

U V

=

=

Locus

The locus are two lines STand UVthatare parallel to AB.

S T

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The locus of a moving point that is at equidistant fromtwo intersecting lines ABand CDis a pair of straightlines which bisect the angles between the two

intersecting lines.

A

BC

D

P Q

R

S

The locus are two straight lines PQand RSwhich bisect theangles between the two intersecting lines.

Locus

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Determine the locus of the points which satisfy the given

condition

A point P moves at adistance of 6 cm from a

fixed point O.

A point P moves such that itis 3 cm from the line AB.

A point P moves such that itis equidistant from two

intersecting line AB and CD.

A point P moves such that itis equidistant from the point

E and F.

A circle with centre O

and a radius 6 cm.

Two straight lines parallel

to AB and 3 cm from lineAB.

Two angle bisectors.The perpendicularbisector of the line EF.

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Constructing the locus

To construct the locus:

Describe or sketch the locus.

Decide on a suitable scale. Construct the locus accurately.

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A circle with pupil B as thecentre and a radius of 1.5 m

1.5 m

Locus ofpupil A

Step 1: Describe or sketch the locus.

Step 2: Decide on a suitable scale.

Step 3: Construct the locusaccurately.

1 cm represent 1 m.

1. Place a pair of compasseson a ruler to measure adistance of 1.5 cm.

2. With the point pupil B ascentre, draw an arc 1.5 cm

from B to form a circle.

3. This is the locus of pupil A.

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Perpendicular bisectorof line XY

|| ||

Locus of S

Step 1: Describe or sketch the locus.

Step 2: Decide on a suitable scale.

Step 3: Construct the locusaccurately.

1 cm represent 1 cm.

1. Set your compasses to alength more than half of XY.Place the point of yourcompasses at X and drawan arc above and below the

line.2. With the same length, place

the point of your compassesat Y and draw two arcs tointersect the first two arcs at

A and B.3. Draw a line through A and

B. This is the locus of S.

A

B

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Two parallel lines at aconstant distance of 1.8 cm

from XY

A

Locus of Z

1.8 cm

1.8 cm

Step 1: Describe or sketch the locus.

Step 2: Decide on a suitable scale.

Step 3: Construct the locusaccurately.

1 cm represent 1 cm.

1. Mark a point A on the line XY.

2. Construct perpendicular

bisectors to the line segmentXA and AY. Mark the points ofthe intersection of theperpendiculars with line XY asB and C.

3. Set your compasses to alength of 1.8 cm. Place thepoint of your compasses at Band draw an arc on theperpendicular above and

below the line. Repeat withthe point of your compassesat C.

4. Draw a line 1.8 cm marks instep 3. This is the locus of Z.

B C

Locus of Z

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Two angle bisectors of theangles formed by the line

PQ and RS

Locus of C

Step 1: Describe or sketch the locus.

Step 2: Decide on a suitable scale.

Step 3: Construct the locusaccurately.

1 cm represent 1 cm.

1. Set a pair of compasses toabout half of the length of OP.

Place the point of yourcompasses at O and draw arcsto cut line OP and OR at A and Brespectively.

2. Place the point of the compassesat A and then at B to draw twoarcs that intersect.

3. Draw a line through O and thepoint where the arcs intersect.

This line is the bisector of POBand SOQ.

4. Use the step 1, 2 and 3 as aguide to draw the bisector of

POS and ROQ. The bisector

of the angles is the locus of C.

O

A

B

Locus of C

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Locus of P

Locus of Q

A

Locus of W1 cm

1 cm

B C

Locus of W

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Locus of Q

1.5 cm

Locus of R

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Locus of S

Locus of T

1 cm

1 cm

Locus of T

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Locus of U

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The intersection of two loci is the point orpoints that satisfy the conditions

of the two loci.

The points of intersection of two loci that is

(a) equidistant from Aand B,(b) a constant distance from A.

X

YEquidistant

from Aand B.

A constantdistance from A.

The points XandYare the points ofintersection of the

two loci.

A

B

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Locus of Y

Locus of X

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Locus of X

Locus of Y

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Locus of X Locus of Y

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Locus of QLocus of P

Two intersection

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Locus of X

|| ||

Locus of Y

Two intersection

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Locus of X

Locus of Z

Locus of Y

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Construct astraight line XYof

length 2.4 cm.Then constructthe locus of point Psuch

that it is always1.5 cm from X.

point Q that isequidistant

from Xand Y.Mark the point ofintersection as Aand B.

X Y2.4 cm

Locus of Q

Locus of P

A

B

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Draw an equilateraltriangle ABCwithsides of length 3 cm.

Then, construct thelocus of point that is

equidistantfrom A andB.

2 cm from B.Mark the point of

intersection as DandE.

A B3 cm

C

3 cm3 cm

D

E