(1) tan角AOB = A的縱坐標(biāo)/ A的橫坐標(biāo) = 2/2sqrt3 = (sqrt3)/3 (sqrt:平方根)
角AOB = 30°
三角形OBA繞點(diǎn)O順時(shí)針旋轉(zhuǎn)30°,A落在B開始的位置,B的新位置與A初始時(shí)的位置關(guān)于x軸對(duì)稱,B'(2sqrt3,-2)
-2 = k/(2sqrt3),k = -4sqrt3
(2)三角形OAB繞O旋轉(zhuǎn)時(shí),A',B'與O的距離總為4(=OA = OB).
設(shè)A'(a,-4sqrt3/a)
OA' = 4 = sqrt(a^2 + 16*3/a^2)
a^2 = 4或a^2 = 12
反比例函數(shù)y=k/x的此一支在第4象限,a > 0
a = 2或a = 2sqrt3
其實(shí)它們就是B'和A'的橫坐標(biāo)
B'(2,-2sqrt3),A'(2sqrt3,-2)
自己驗(yàn)證AB = A'B'.