(1)如图
(2)可设C点坐标为(m, n) ∵C到轴的距离为1,到轴的距离为 ∴|m| = , |n| = 1
∴ m = ± ,n = ± 1
∵ 点是第二象限内的点 ∴C点坐标为(-, 1)
点当x = -时, y = -×2 = 1 ∴点C在直线上
(3)存在, ∵ |CD| =1,|OA| = 1,
∴ |CD| = |OA|
又∵点P在x轴上
∴∠CDP = 90°= ∠AOB 若 |DP| = |OB| = 2 时,可用SAS证明△CDP≌△AOB,
∴当P点坐标为(-+2,0)或(--2,0)时, 即P点坐标为(,0)或(-,0)时,
△CDP≌△AOB
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