數學坐標計算問題

5.
(a)
M 點坐標 = ([4-1]/2, [8+3]/2)= (3/2, 11/2)

(b)
N 點坐標 = ([-1*3+4*2]/[3+2],[3*3+8*2]/[3+2]) = (1, 5)


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6.
(-5 - 10)/(a - 3) = (-5 - 7)/(-3 - 1)
-15/(a - 3) = 3
3a - 9 = -15
3a = -6
a = -2


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7.
垂直 L 直線的斜率 = (2 + 4)/(5 - 2) = 2

L 的斜率 = -1/2


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8.
tan60° = (0+ 2n)/[(√3)n +2(√3)]
√3 = 2n/[(√3)n + 2(√3)]
3n + 6 = 2n
n = -6


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9.
設 B 的坐標為 (p, q)。

[1(-1) + 3*p]/(3 + 1) = 2
(3p -1)/4 = 2
3p - 1 = 8
3p = 9
p = 3

[1*(-4) + 3*q]/(3 + 1) = -1
(3q - 4)/4 = -1
3q - 4 = -4
q = 0

B 的坐標 = (3,0)


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10.
(a)
AB = √[(1 +1)² + (-2- 2)²] = √20 = 2√5

BC = √[(-2- 0)² + (1 - 5)²] = √20 = 2√5

AC = √[(-1+ 5)² + (2- 0)²] = √40 = 2√10

(b)
AB 斜率 = (2 + 2)/(-1 -1) = -2

BC 斜率 = (-2 + 0)/(1 -5) = 1/2


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11.
(a)
AD 斜率 = (1 + 4)/(4 +1) = 1
AB 斜率 = (y - 1)/(-1)= 1 - y


1 * (1 - y) = -1
1 - y = -1
y = 2

(b)
設 C 的坐標為 (c, 0)。

BC斜率 = AD斜率
(2 - 0)/(3 - c) = 1
3 - c = 2
c = 1


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12.
(a)
AB = √[(1 + 3)² + (1 - 5)²] = √32 = 4√2

BC = √[(-3 - 1)² + (5 - 9)²] = √32 = 4√2

CD = √[(5- 1)² + (5 - 9)²] = √32 = 4√2

AD = √[(5- 1)² + (5 - 1)²] = √32 = 4√2

(b)
AB 斜率 = (1 + 3)/)1 - 5) = -1

BC 斜率 = (1 + 3)/(9 - 5) = 1

CD 斜率 = (5 - 1)/(5 - 9) = -1

DA 斜率 = (5 - 1)/(5 - 1) = 1