a-maths~~~~~

(a) 2x-y = 0 ...(1)
3x+y - 10 = 0 ...(2)
(1): y = 2x
代此入(2): 3x+ 2x - 10 =0
5x = 10
x = 2
y = 2(2) = 4
A的坐標是(2, 4)
由於AD是三角形的高,H必定通過AD.
點A和點H的x坐標都是2, 所以AD方程是 x = 2.
(b) AC斜率 = -3
BE的斜率 = -1/(-3) = 1/3
BE會通過H, 所以BE方程:
y+1 = (1/3)(x-2)
3y+3 = x-2
x-3y-5 = 0
求B的坐標, 解聯立方程2x- y = 0 及x -3y - 5 = 0
x - 3(2x) - 5 = 0
5x = -5
x = -1
y = 2(-1) = -2
B的坐標是(-1, -2)
(c) AB的斜率 = 2
CF的斜率 = -1/2
CF的方程 : y+1 = -1/2 (x-2)
-2y-2 = x-2
x+2y = 0
解x+2y = 0 及3x+y -10 = 0
3(-2y) + y - 10 = 0
5y = -10
y = -2
x = -2(-2) = 4
C的坐標是(4, -2)
B和C的y坐標是-2
所以BC的方程是y = -2