In a polar coordinate system, the polar coordinates of the points P, Q and R are (5, 133o), (4, 223o) and (7, 313o) respectively. Let O be the pole.
(a)Is PR perpendicular to QO? Explain your answer.
(b)Find the area of PQR.
(Yes; 24 sq. units; i want to know how to find the slopes of PR and QO)
(a)Find the average speed of Patrick in the period in km/h.
(b)When do Patrick and Queenie meet during the period?
(c)If the average speed of Queenie after the rest is 9 km/h, how long does she rest?
(d)Patrick claims that his average speed is higher than that of Queenie during the period 2:40 to 3:30 in the afternoon. Do you agree? Explain your answer.
https://www.flickr.com/photos/130230543@N06/16159535940/
(6 km/h; 2:50 p.m. ; 30 min ; Yes; just go straight to part b to d)
1_PEE_LBP_E.doc
2015-01-24 3:07 am
回答 (3)
2015-01-24 10:19 am
✔ 最佳答案
1.(a)
∠POQ = 223° - 133° = 90°
Hence, OQ⊥OP
∠QOR = 313° - 223° = 90°
Hence, OQ⊥OR
Since OQ⊥OP and OQ⊥OR
then, POR is a st. line, and PR⊥OQ
(b)
Since POR⊥OQ, then OQ is the height of ΔPQR from Q.
Area of ΔPQR
= (1/2) × PR × OQ
= (1/2) × (5 + 7) × 4
= 24 square units
====
2.
(a)
Speed of Patrick
= Distance / Time
= 9 / (3.5 - 2) km/h
= 6 km/h
(b)
When they meet:
Distance travels of Queenie = 4 km
Distance travels of Patrick = (9 - 4) km = 5 km
Time taken when they meet = 5/6 h = 50 min
Time when they meet = 2:50
(c)
Total time taken of Queenie = (3.5 - 2) h = 1.5h = 90 min
Time taken before Queenie rests = 40 min
After rest, Queenie travels (7 - 4) km = 3 km
Time taken after the rest = 3/9 h = 1/3 h = 20 min
Period that Queen rests = (90 - 40 - 20) min = 30 min
(d)
During the period 2:40 to 3:30 :
Distance travels of Queenie = (7 - 4) km = 3 km
Time taken of Queenie = (60 - 40 + 30) = 50 min = 5/6 h
Average speed of Queenie = 3 / (5/6) km/h = 3.6 km/h
Average speed of Patrick = 6 km/h > 3.6 km/h
Hence, I agree what Patrick claims.
2015-01-24 8:03 am
Note that 313o = 133o + 180o and 223o = 133o + 90o
2015-01-24 4:33 am
You may consider ∠POQ only without finding the slopes of PR and QO.
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