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

A figure of ‘8’ A circle

circle

vertical line pentagon

square triangle

curve / arc

Describe and sketch the locus of the moving point The tip of a minute hand rotating on the face of a

clock. 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

A swinging pendulum.

An arc

The centre of the wheel of a moving vehicle on the road.

A horizontal straight line

A competitor running in a 400 m race in the field.

An oval

Exercise:

9.1A Question 2 9.1B All

The locus of a moving point P that is at a constant distance from a fixed point O is a circle with centre O.

O

P

Locus of P

The locus of P is a circle with radius OP and centre O.

The locus of a moving point R equidistant from two fixedpoints A and B is the perpendicular bisector of the lineAB.

|| ||

The locus of R is the perpendicular bisector of AB.

A B

Locus of R

The locus of a moving point that is a constant distance from a straight line AB are two straight lines that are parallel toAB.

A B

U V

=

=

Locus

The locus are two lines ST and UV that are parallel to AB.

S T

The locus of a moving point that is at equidistant fromtwo intersecting lines AB and CD is a pair of straightlines which bisect the angles between the twointersecting lines.

A

BC

D

P Q

R

S

The locus are two straight lines PQ and RS which bisect theangles between the two intersecting lines.

Locus

Determine the locus of the points which satisfy the given condition

A point P moves at a distance of 6 cm from a fixed point O.

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

A point P moves such that it is equidistant from two intersecting line AB and CD.

A point P moves such that it is 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 line AB.

Two angle bisectors. The perpendicular bisector of the line EF.

Constructing the locusConstructing the locus

To construct the locus: Describe or sketch the locus. Decide on a suitable scale. Construct the locus accurately.

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

1.5 m

Locus of pupil A

Step 1: Describe or sketch the locus.

Step 2: Decide on a suitable scale.

Step 3: Construct the locus accurately.

1 cm represent 1 m.

1. Place a pair of compasses on a ruler to measure a distance of 1.5 cm.

2. With the point pupil B as centre, draw an arc 1.5 cm from B to form a circle.

3. This is the locus of pupil A.

Perpendicular bisector of line XY

|| ||

Locus of S

Step 1: Describe or sketch the locus.

Step 2: Decide on a suitable scale.

Step 3: Construct the locus accurately.

1 cm represent 1 cm.

1. Set your compasses to a length more than half of XY. Place the point of your compasses at X and draw an arc above and below the line.

2. With the same length, place the point of your compasses at Y and draw two arcs to intersect the first two arcs at A and B.

3. Draw a line through A and B. This is the locus of S.

A

B

Two parallel lines at a constant 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 locus accurately.

1 cm represent 1 cm.

1. Mark a point A on the line XY.

2. Construct perpendicular bisectors to the line segment XA and AY. Mark the points of the intersection of the perpendiculars with line XY as B and C.

3. Set your compasses to a length of 1.8 cm. Place the point of your compasses at B and draw an arc on the perpendicular above and below the line. Repeat with the point of your compasses at C.

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

B C

Locus of Z

Two angle bisectors of the angles 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 locus accurately.

1 cm represent 1 cm.

1. Set a pair of compasses to about half of the length of OP. Place the point of your compasses at O and draw arcs to cut line OP and OR at A and B respectively.

2. Place the point of the compasses at A and then at B to draw two arcs that intersect.

3. Draw a line through O and the point where the arcs intersect. This line is the bisector of POB and SOQ.

4. Use the step 1, 2 and 3 as a guide to draw the bisector of POS and ROQ. The bisector of the angles is the locus of C.

O

A

B

Locus of C

||

||

Locus of P

Locus of Q

A

Locus of W1 cm

1 cm

B C

Locus of W

Locus of Q

1.5 cm

Locus of R

Locus of S

Locus of T

1 cm

1 cmB

C

Locus of T

Locus of U

The intersection of two loci is the point or points that satisfy the conditions

of the two loci.

The points of intersection of two loci that is(a) equidistant from A and B,(b) a constant distance from A.

X

YEquidistantfrom A and B.

A constant distance from A.

The points X andY are the points ofintersection of the

two loci.A ×

B×

Locus of Y

Locus of X

Locus of X

Locus of Y

||

||Locus of X

Locus of Y

Locus of QLocus of PTwo intersection

Locus of X

|| ||

Locus of Y

Two intersection

Locus of X

Locus of Z

Locus of Y

Construct a straight line XY of length 2.4 cm. Then construct the locus of • point P such that it is always 1.5 cm from X.• point Q that is equidistant from X and Y.Mark the point of intersection as A and B.

X Y2.4 cm

Locus of Q

Locus of P

A

B

Draw an equilateral triangle ABC with sides of length 3 cm. Then, construct the locus of point that is

• equidistant from A and B.• 2 cm from B.

Mark the point of intersection as D and E.

A B3 cm

C

3 cm3 cm

D

E