Question

已知直角坐标平面内的点A(-3,2)、B(1,4),在x轴上求一点C,使得△ABC是等腰三角形.

Answer 1

设点C为(a,0),

(1)AB=AC

(-3-1)^2+(2-4)^2=(-3-a)^2+2^2

a=-7或者a=1

C(-7,0)或(1,0)

(2)AB=BC

(-3-1)^2+(2-4)^2=(1-a)^2+4^2

a=3或a=-1

C(3,0)或(-1,0)

(3)AC=BC

(-3-a)^2+2^2=(1-a)^2+4^2

a=1/2

C(1/2,0)