直角坐標數學題(((超超超超急!!唔該快!!!!))))

1)已知abcd為長方型,若a丶b同c公別為(1,1)丶(1,6)同(3,6),求d的坐標。
Let d be (x,y),
Slope of ab = Slope of cd,
(6-1)/0 = (6-y)/(3-x)
15-5x = 0
x = 3
Slope of bc = Slope of ad,
(6-6)/(3-1) = (y-1)/(x-1)
0 = 2y - 2
y = 1
d:(3,1)
2)梯型各頂點的坐標分別為A(-2,-1)丶b(5,1)丶c(3,2)同d(-1,2)，求梯型的面積。
梯型的面積
= 1/2 |3 2|
|5 1|
|-1 2|
|-2 -1|
|3 2|
= 1/2 *(3*1 + 5*2 + -1*-1 + -2*2 - 3*-1 - -2*2 - -1*1 - 5*2)
= 1/2 *(3+10+1-4+3+4+1-10)
= 1/2 *(8)
= 4 sq units.
3)已知a(-5,-2) 同b(x,-2)之間的距離為6單位。b的坐標是否唯一的?簡述你的答案。
ab = 6
√[(-5-x)^2 + (-2+2)^2] = 6
x^2 + 10x + 25 = 36
x^2 + 10x - 11 = 0
(x+11)(x-1) = 0
x = -11 or 1
Since x has two solutions, b is only one.
4)下列哪點不在y軸上?
a.(0,-2)
b.(0,2)
c.(0,0)
d.(2,0)
When the point lies on y-axis,
x = 0, Therefore, a,b,c are all lies on y-axis.
Answer = D.
5)下列哪點在x軸上?
a (-1,-1)
b (0,-1)
c (-1,0)
d (1,-1)
When the point lies on x-axis,
y = 0,
Only answer c has the y-coordinate is 0,
Answer: C