數學[續坐標]一問 - Ans.fyi 參考答案

數學[續坐標]一問

pinky9410

2009-07-05 10:00 pm

1) A(a,8)和B(4,2)的距離是10。求 a 的兩個可能值。

2) 若A(4,2)、B(4,-1)、C(-2,-1)與D為某矩形的四個頂點，求D的坐標和矩形的面積。

3a) 求以(1,1)、(1,-2)與(5,-2)為頂點的三角形的周界。

3b) 求以上三角形重心的坐標。

4) A(-1,2)、B(-2,-1)、C(2,-2)及D(3,1)為一個四邊形的頂點。試求出每條邊的斜率,以證明ABCD是一個平行四邊形。

5) P是CD上的一點，且CP:CD=2:3。求P點的坐標。

回答 (1)

Jack

2009-07-06 12:01 am

✔ 最佳答案

1. 10^2 = (8-2)^2 + (a-4)^2 => 64 = (a-4)^2 => a = -4 or 12

2. D = (-2, 2) (Just look at the figures and you can see it, each number appear twice. Isn't it funny!)

3a. It is a 3-4-5 直角三角形 => 周界 = 3+4+5=12
3b. 重心坐標 = (-2, 1) (Just draw it, and again you will see!)

4. Slope = (delta y)/(delta x)
Slope of AD = (2)-(1) / (-1)-(3) = -1/4
Slope of BC = (-1)-(-2) / (-2)-(2) = -1/4
Slope of AB = (2)-(-1) / (-1)-(-2) = 3
Slope of DC = (1)-(-2) / (3)-(-2) = 3
Since Slope of AD = Slope of BC & Slope of AB = Slope of DC. Therefore, ABCD is a 平行四邊形.

5. Let C=(c1,c2), D=(d1,d2) & P=(p1,p2)
CP:CD=2:3
=> p1 = c1 + (d1-c1)x2/(2+3) = 0.6 x c1 + 0.4 x d1
& p2 = c2 + (d2-c2)x2/(2+3) = 0.6 x c2 + 0.4 x d2
Therefore, P=(0.6 x c1 + 0.4 x d1, 0.6 x c2 + 0.4 x d2)
eg.,
If C=(2,-2) & D=(3,1)
Then P=(0.6x2+0.4x3, 0.6x(-2)+0.4x1)=(2.4,-0.8)

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