Rosila
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Transcript of Rosila
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