Question

如图 ,一次函数y=1/3x+b的图像与x轴相交于点A(6,0),与y轴相交于点B,点C在y轴的

如图，一次函数y=
1
3
x+b的图象与x轴相交于点A（6，0）、与y轴相交于点B，点C在y轴的正半轴上，BC=5．
（1）求一次函数的解析式和点B、C的坐标；
（2）如果四边形ABCD是等腰梯形，求点D的坐标．
D有两个坐标的。

Answer 1

(1) x = 6, y = 6/3 + b = 2 + b = 0, b = -2
y = x/3 - 2
B(0,-2)
C(0, c), c > 0
BC = c -(-2) = c + 2 = 5, c = 3
C(0, 3)

(2)图自己画，有两种可能：
(a) AD//BC, CD = AB
AB² = (-2)² + 6² = 40
D(6, d)
CD² = (0 - 6)² + (3 - d)² = 36 + (3 - d)² = 40
d = 1 (舍去d = 5，此时ABCD为平行四边形)
D(6, 1)

(b) CD//BA, BC = AD
BC² = 25
CD的方程: y = x/3 + 3
D(d, d/3 + 3)
AD² = (d - 6)² + (d/3+ 3- 0)² = 25
d² - 9d + 18 = (d - 3)(d - 6) = 0
d = 3 (舍去d = 6，此时ABCD为平行四边形)
D(3, 4)