He politely asked her out, but she abruptly rejected his invitation.

rejected 是动词 reject 的过去式。reject 由前缀 re-（表示"回、反"）和词根 ject（来自拉丁语 jacere，意为"投掷"）组成，字面意思是"扔回去"，引申为"拒绝、不接受"的意思。在这里表示"拒绝了他的邀请"。