第5題   a-b為多少?

5.
AD//BC
AD的斜率 = BC的斜率
(b - 3)/(a + 2) = (-4 + 10)/(-7 - 3)
(b - 3)/(a + 2) = -3/5
5b - 15 = -3a - 6
3a + 5b = 9 …… [1]

DC//AB
DC的斜率 = AB的斜率
(b + 10)/(a - 3) = (3 + 4)/(-2 + 7)
(b + 10)/(a - 3) = 7/5
5b + 50 = 7a - 21
7a - 5b = 71 …… [2]

[1] + [2]:
10a = 80
a = 8

將 a = 8 代入 [1] 中:
3(8) + 5b = 9
5b = -15
b = -3

所以，a - b
= 8 - (-3)
= 11

最簡單就是AC中點=BD中點
x_A+x_C=x_B+x_D；y_A+y_C=y_B+y_D
得a=8、b=-3，則a-b=11