F.3 MATH (直角坐標幾何)

用戶40111

2009-12-11 6:27 am

1.

圖片參考：http://i305.photobucket.com/albums/nn203/iris993/1719825d.jpg

(b) [ 答案 = ( -1 , -3 ) ]
(c) [ 答案 = ( 3 , -1 ) ]

2.求 P 點的坐標
(a) A (5 , -7) , B (-1 , 3)；PB = 3/4 AB
[ 答案 = ( 11/2, 4) ]

(b) A (-5 , 9) , B (15 , -11)；PB = 1/5 AB
[ 答案 = ( -3 , 11/2) ]

(c) A (-9 , 5) , B (-1 , 1)；AP = 5/8 AB
[ 答案 = ( 6 , 5 ) ]

3. 已知 A ( 0 , 6 )、B ( x , 2 ) 和 P ( 4 , y ) 三點，若P點為線段 AB 的中點，求 x 和 y 的值。
[ 答案 : x = 8 , y = 4 ]

回答 (1)

用戶9112

2009-12-11 6:47 am

✔ 最佳答案

(1)(b) x = (-4 + 2)/2 = -1
y = (-2 - 4)/2 = -3
P = (-1, -3)
(c) x = (-4 + 10)/2 = 3
y = (4 - 6)/2 = -1
P = (3,-1)
(2) 提供答案不對
(a) PB = (3/4)AB => AP : PB = 1 : 3
x = [(3)(5) + (1)(-1)] / (1 + 3) = 7/2
y = [(3)(-7) + (1)(3)] / (1 + 3) = -9/2
P = (3.5, -4.5)
(b) PB = (1/5)AB => AP : PB = 4 : 1
x = [(1)(-5) + (4)(15)] / (4 + 1) = 11
y = [(1)(9) + (4)(-11)] / (4 + 1) = -7
P = (11, -7)
(c) AP = (5/8)AB => AP : PB = 5 : 3
x = [(3)(-9) + (5)(-1)] / (5 + 3) = -4
y = [(3)(5) + (5)(1)] / (5 + 3) = 2.5
P = (-4, 2.5)
(3) 4 = (0 + x)/2 => x = 8
y = (6 + 2)/2 = 4

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