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math's Q

2013-11-25 12:54 am

Q1) In the polar coordinate plane,
coordinate O is ( 0, 0° )
coordinate P is (3, 60°)
coordinate Q is (3, 150°)

Angle POQ is 90°

How to find the length of PO and QO?
How to find the area of triangle OPQ?

Q2) A(3,0) and B(1,4) are two points in a retangular coordinate plane.
Suppose A' is the image obtained by reflecting A along the straight line y=k,
where k is a constant and k>0.

(a) Write down the coordinates of A' in terms of k.

(b) If AB and A'B are perpendicular to each other, find the value of k.

回答 (1)

用戶4366

2013-11-25 1:37 am

✔ 最佳答案

Q1How to find the length of PO and QO?
PO = 3
QO = 3

angle POQ = 150⁰ - 60⁰ = 90⁰

Area of triangle OPQ = (1/2)(PO)(QO) = (1/2)(3)(3) = 4.5 square unit.

Q2. A' is (3,2k)

slope of AB = (4-0)/(1-3) = -(4/2) = -2
slope of A'B = (2k-4)/(3-1) = 2(k-2)/2 = k-2

since AB perpendicular to A'B

(-2)(k-2) = -1
-2k+4 = -1
5 = 2k
k = 5/2

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