HKCEE 數學 Past Paper 問題. [20分]
2012-02-17 10:12 am
圖片參考：http://upload.lyfhk.net/di-G4LZ.jpg
In Figure 5, A(-8, 8) and B(16,-4) are two points.
The perpendicular bisector L of the line segment AB
cuts AB at M and the x-axis at P.
(a) Find the equation of L.
Slope of AB = -0.5
Slope of L = 2
Coord. of M = (4,2)
The equation of L: 2x - y -6 = 0
(b) Find the length of BP.
Coord. of P = (3,0)
Length of BP: 185^0.5
(c) If N is the mid-point of AP, find the length of MN.
(請解答 c部分)
回答 (1)
2012-02-18 2:04 am
✔ 最佳答案
(Quick Method) :As N is the mid-pt of AP and APM is a right-angled triangle, so
MN = NA = NP = 0.5BP
therefore, the length of MN = 0.5 √185
(Normal Method) :
Co-ordinate of N is (0.5*(-8 + 3), 0.5*(8 + 0)) = (-2.5, 4)
Therefore, the length of MN is :
√[(4 + 2.5)^2 + (2 - 4)^2]
= √(42.25 + 4)
= 0.5√185
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