Math Mf2 Chapter 9 (loci In Two Dimensions)
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PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
PMR questions. 1. Diagram 1 in the answer space shows four squares, PKJN, KQLJ, NJMS and JLRM. W, X and Y are three moving points in the diagram. (a) W moves such that it is equidistant from the straight lines PS and QR. By using the letters in the diagram, state the locus of W. (b) On the diagram, draw i) the locus of X such that XJ = JN, ii) the locus of Y such that its distance from point Q and point S are the same. (c) Hence, mark with the symbol ⊗ all the intersections of the locus of X and the locus of Y. Answer: P
N
S
K
J
Q
P
S
Q
R
L
M Diagram 1
R
Diagram 2
2. Diagram 2 in the answer space shows a squares, PQRS drawn on a grid of equal squares with sides of 1 unit. M, X and Y are three moving points in the diagram. (a) M is the point which moves such that its distance from point Q and point S are the same. By using the letters in the diagram, state the locus of M. (b) On the diagram, draw i) the locus for the point X that is constantly 5 units from the line QR, ii) the locus for the point Y that is constantly 7 units from the point R. (c) Hence, mark with the symbol ⊗ the intersections of the locus of X and the locus of Y.
1
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
3. Diagram 3 in the answer space shows a squares, PQRS drawn on a grid of equal squares with sides of 1 unit. W, X and Y are three moving points in the diagram. (a) W is the point which moves such that it is equidistant from the straight lines PQ and PS. By using the letters in the diagram, state the locus of W. (b) On the diagram, draw i) the locus for the point X that is constantly 5 units from the point P, ii) the locus for the point Y that is constantly 4 units from the straight line QR. (c) Hence, mark with the symbol ⊗ the intersections of the locus of X and the locus of Y. Answer:
Q
P
R
S Diagram 3
4. (a) Diagram 4 shows a rhombus MNOP. X is a moving point in the rhombus such that it is always equidistant from the straight lines PM and PO. By using the letters in the diagram, state the locus of X. (b) Diagram 5 in the answer space shows a regular hexagon ABCDEF. Y and Z are two moving points in the hexagon. On diagram 5, draw i) the locus of Y such that YD = DE, ii) the locus of Z such that it is equidistant from point B and point F. (c) Hence, mark with the symbol ⊗ the intersections of the locus of Y and the locus of Z.
2
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
Answer: B
A
N
M
F
P
C
E
O
D
Diagram 5
Diagram 4
5. Diagram 6 in the answer space shows a circle with centre O, drawn on a grid of equal squares with sides of 1 unit. AOB is a diameter of the circle. X, Y and Z are three moving points inside the circle. (a) X is the point which moves such that it is constantly 3 units from the point O. Describe fully the locus of X. (b) On diagram 6, draw i) the locus of the point Y which moves such that its distance is constantly 2 units from the line AB. ii) the locus of the point Z which moves such that it is equidistant from the point A and the point B. (c) Hence, mark with the symbol ⊗ the intersections of the locus of Y and the locus of Z. Answer:
A
O
B
Diagram 6
3
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
Module questions. 6. Diagram 7 in the answer space shows a rhombus, JKLM. W, X and Y are three moving points in the diagram. (a) W is the point which moves such that it is equidistant from the straight lines JK and KL. By using the letters in the diagram, state the locus of W. (b) On the diagram, draw i) the locus for the point X that is equidistant from the straight lines JL and KM, ii) the locus for the point Y that is constantly 3 cm from the intersecting point of straight line JL and KM. (c) Hence, mark with the symbol ⊗ the intersections of the locus of X and the locus of Y. Answer:
K
J
L
M Diagram 7 7. Diagram 8 in the answer space shows four squares, PQRS with the centre O. T, U, V and W are the midpoints of PQ, QR, RS and PS respectively. X, Y and Z are three moving points in the diagram. (a) X moves such that it is equidistant from the straight lines PQ and SR. By using the letters in the diagram, state the locus of X. (b) On the diagram, draw i) the locus of Y such that OY = OT, ii) the locus of Z such that its distance from point P and point R are the same. (c) Hence, mark with the symbol ⊗ all the intersections between locus Y and locus Z.
4
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
Answer: T
P
W
Q
U
O
S
V
R
Diagram 8 8. Diagram 9 in the answer space shows two rectangles PQRS and QTUR. A, B and C are three moving points in the diagram. (a) A is the point which moves such that it is equidistant from the straight lines PS and TU. By using the letters in the diagram, state the locus of A. (b) On the diagram, draw i) the locus of B such that it is always 3 cm from the straight line QR, ii) the locus of C such that it is equidistant from the straight lines PQT and SRU. (c) Hence, mark with the symbol ⊗ the intersections of the locus of B and C. Answer:
P
Q
T
S
R
U
Diagram 9
5
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
9. Diagram 10 in the answer space shows a squares, PQRS drawn on a grid of equal squares with sides of 1 unit. A, B and C are three moving points in the diagram. (a) Point A is the point which moves such that its distance from the straight lines QR and RS is the same. By using the letters in the diagram, state the locus of A. (b) On the diagram, draw i) the locus for the point B that is constantly 7 units from the point R, ii) the locus for the point C such that CT = PT. (c) Hence, mark with the symbol ⊗ the intersections of the locus of B and the locus of C. Answer: P
T
Q
A
B
H
R
S
Diagram 10
C
D
J
G
F
E
Diagram 11
10.Diagram 11 in the answer space shows four squares, ABJH, BCDJ, HJFG and JDEF. W, X and Y are three moving points in the diagram. (a) W is the point which moves such that it is equidistant from the straight lines AC and EG. By using the letters in the diagram, state the locus of W. (b) On the diagram, draw i) the locus of X such that XJ = JB, ii) the locus of Y such that YF = GF. (c) Hence, mark with the symbol ⊗ the intersections of the locus of X and the locus of Y.
6
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
PMR questions. 1. Diagram 1 in the answer space shows four squares, PKJN, KQLJ, NJMS and JLRM. W, X and Y are three moving points in the diagram. (a) W moves such that it is equidistant from the straight lines PS and QR. By using the letters in the diagram, state the locus of W. (b) On the diagram, draw i) the locus of X such that XJ = JN, ii) the locus of Y such that its distance from point Q and point S are the same. (c) Hence, mark with the symbol ⊗ all the intersections of the locus of X and the locus of Y. Answer: P
N
S
K
J
Q
P
S
Q
R
L
M Diagram 1
R
Diagram 2
2. Diagram 2 in the answer space shows a squares, PQRS drawn on a grid of equal squares with sides of 1 unit. M, X and Y are three moving points in the diagram. (a) M is the point which moves such that its distance from point Q and point S are the same. By using the letters in the diagram, state the locus of M. (b) On the diagram, draw i) the locus for the point X that is constantly 5 units from the line QR, ii) the locus for the point Y that is constantly 7 units from the point R. (c) Hence, mark with the symbol ⊗ the intersections of the locus of X and the locus of Y.
1
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
3. Diagram 3 in the answer space shows a squares, PQRS drawn on a grid of equal squares with sides of 1 unit. W, X and Y are three moving points in the diagram. (a) W is the point which moves such that it is equidistant from the straight lines PQ and PS. By using the letters in the diagram, state the locus of W. (b) On the diagram, draw i) the locus for the point X that is constantly 5 units from the point P, ii) the locus for the point Y that is constantly 4 units from the straight line QR. (c) Hence, mark with the symbol ⊗ the intersections of the locus of X and the locus of Y. Answer:
Q
P
R
S Diagram 3
4. (a) Diagram 4 shows a rhombus MNOP. X is a moving point in the rhombus such that it is always equidistant from the straight lines PM and PO. By using the letters in the diagram, state the locus of X. (b) Diagram 5 in the answer space shows a regular hexagon ABCDEF. Y and Z are two moving points in the hexagon. On diagram 5, draw i) the locus of Y such that YD = DE, ii) the locus of Z such that it is equidistant from point B and point F. (c) Hence, mark with the symbol ⊗ the intersections of the locus of Y and the locus of Z.
2
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
Answer: B
A
N
M
F
P
C
E
O
D
Diagram 5
Diagram 4
5. Diagram 6 in the answer space shows a circle with centre O, drawn on a grid of equal squares with sides of 1 unit. AOB is a diameter of the circle. X, Y and Z are three moving points inside the circle. (a) X is the point which moves such that it is constantly 3 units from the point O. Describe fully the locus of X. (b) On diagram 6, draw i) the locus of the point Y which moves such that its distance is constantly 2 units from the line AB. ii) the locus of the point Z which moves such that it is equidistant from the point A and the point B. (c) Hence, mark with the symbol ⊗ the intersections of the locus of Y and the locus of Z. Answer:
A
O
B
Diagram 6
3
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
Module questions. 6. Diagram 7 in the answer space shows a rhombus, JKLM. W, X and Y are three moving points in the diagram. (a) W is the point which moves such that it is equidistant from the straight lines JK and KL. By using the letters in the diagram, state the locus of W. (b) On the diagram, draw i) the locus for the point X that is equidistant from the straight lines JL and KM, ii) the locus for the point Y that is constantly 3 cm from the intersecting point of straight line JL and KM. (c) Hence, mark with the symbol ⊗ the intersections of the locus of X and the locus of Y. Answer:
K
J
L
M Diagram 7 7. Diagram 8 in the answer space shows four squares, PQRS with the centre O. T, U, V and W are the midpoints of PQ, QR, RS and PS respectively. X, Y and Z are three moving points in the diagram. (a) X moves such that it is equidistant from the straight lines PQ and SR. By using the letters in the diagram, state the locus of X. (b) On the diagram, draw i) the locus of Y such that OY = OT, ii) the locus of Z such that its distance from point P and point R are the same. (c) Hence, mark with the symbol ⊗ all the intersections between locus Y and locus Z.
4
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
Answer: T
P
W
Q
U
O
S
V
R
Diagram 8 8. Diagram 9 in the answer space shows two rectangles PQRS and QTUR. A, B and C are three moving points in the diagram. (a) A is the point which moves such that it is equidistant from the straight lines PS and TU. By using the letters in the diagram, state the locus of A. (b) On the diagram, draw i) the locus of B such that it is always 3 cm from the straight line QR, ii) the locus of C such that it is equidistant from the straight lines PQT and SRU. (c) Hence, mark with the symbol ⊗ the intersections of the locus of B and C. Answer:
P
Q
T
S
R
U
Diagram 9
5
PMR Question Module Chapter 9 Form 2 2009
compeil@smkpb
Mathematics : Loci in Two Dimensions Answer all questions.
9. Diagram 10 in the answer space shows a squares, PQRS drawn on a grid of equal squares with sides of 1 unit. A, B and C are three moving points in the diagram. (a) Point A is the point which moves such that its distance from the straight lines QR and RS is the same. By using the letters in the diagram, state the locus of A. (b) On the diagram, draw i) the locus for the point B that is constantly 7 units from the point R, ii) the locus for the point C such that CT = PT. (c) Hence, mark with the symbol ⊗ the intersections of the locus of B and the locus of C. Answer: P
T
Q
A
B
H
R
S
Diagram 10
C
D
J
G
F
E
Diagram 11
10.Diagram 11 in the answer space shows four squares, ABJH, BCDJ, HJFG and JDEF. W, X and Y are three moving points in the diagram. (a) W is the point which moves such that it is equidistant from the straight lines AC and EG. By using the letters in the diagram, state the locus of W. (b) On the diagram, draw i) the locus of X such that XJ = JB, ii) the locus of Y such that YF = GF. (c) Hence, mark with the symbol ⊗ the intersections of the locus of X and the locus of Y.
6
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