✔ 最佳答案
求證平衡四邊形: AB 同CD既Slope/距離係一樣
求證長方形 : AB同BC 既slope 相乘係-1
求證菱形: 四邊距離相等(PQ=QR=RS=ST
求正方形: 鄰邊(如PQ及QR)Slope相乘=-1
以下M = Slope of (xx), D = Distance of (xx)
1: M (AB)= -2-1/-1-(-2) = -3
M(CD)= 3-0/4-5 = -3
D(AB) = root of [-2-(-1)]²+[1-(-2)]² = root 10
D (CD)= root of [5-4]²+[0-3]² = root 10
ABCD is a parallelogram
b) M (AB)= -3
M (BC)= 0-(-2)/5-(-1) = 1/3
M (AB) x M (CD) = -1
ABCD is a rectangle
2:
D(PQ)= root 3²+1² = root 10
D(QR)= root [3-2]²+[1-4]² = root 10
D(RS)= root [2-(-1)]² + [4-3]² = root 10
D(SP)= root [-1]²+[3]² = root 10
其實已經可以prove PQRS is a rhombus
b) M (PQ)= 1/3
M (QR)= 4-1/2-3 = 3/-1 = -3
M (PQ)x M (QR) = -1
Therefore PQRS is a square
2007-05-03 17:26:52 補充:
Slope A乘Slope B=-1 的話A 同B 成90度