求滿足下列各組條件的直綫方程20分

cheung

2008-10-13 9:01 pm

1.穿過A(1,2)且平行於L:3x+4y-2=0
2.穿過C(3,-1)且垂直於L:2x+y-7=0
3.穿過Q(-2,3)且平行於穿過A(5,7)和B(-1,3)的直綫
4.穿過A(-1,-3)且垂直於穿過P(2,-1)和Q(-4,2)的直綫

回答 (1)

Uncle Michael

2008-10-13 9:43 pm

✔ 最佳答案

1.
L 的斜率 = -3/4
所求直線的斜率 = -3/4

所求的直線方程:
y - 2 = (-3/4)(x - 1)
4(y - 2) = -3(x - 1)
4y - 8 = -3x + 3
3x + 4y - 11 = 0

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2.
L 的斜率 = -2
所求直線的斜率 = 1/2

所求的直線方程:
y + 1 = (1/2)(x - 3)
2(y + 1) = x - 3
2y + 2 = x - 3
x - 2y - 5 = 0

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3.
AB 的斜率
= (7 - 3)/(5 + 1)
= 2/3

所求直線的斜率 = 2/3

所求直線方程:
y - 3 = (2/3)(x + 2)
3(y - 3) = 2(x + 2)
3y - 9 = 2x + 4
2x - 3y + 13 = 0

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4.
PQ 的斜率
= (-1 - 2)/(2 + 4)
= - 1/2

所求直線的斜率 = 2

所求直線方程:
y + 3 = 2(x + 1)
y + 3 = 2x + 2
2x - y - 1 = 0
=

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