F.3 Coordinate Geometry (20 分)

2010-01-25 12:48 am
F.3 Coordinate Geometry of Straight Lines (II) 20 points
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2010-01-25 2:51 am
✔ 最佳答案

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a)
M is ( (a+b)/2 , (0+c)/2 )

M is ( (a+b)/2 , c/2)

b)i)
OA = a , OB = √[(b-0)^2 + (c-0)^2] = √(b^2 + c^2)

OA = OB

a = √(b^2 + c^2)

a^2 = b^2 + c^2

ii)
The slope of AB = (c - 0) / (b - a) = c / (b - a)

The slope of OM = (c/2 - 0) / [ (a+b)/2 - 0 ] = (c/2) / [(a+b)/2] = c / (a + b)

The slope of AB x The slope of OM

= [ c / (b - a) ] [ c / (a + b) ]

= c^2 / (b^2 - a^2)

= c^2 / - c^2 ......(By b i) result)

= - 1

Thus OM丄AB










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