She was at the point of giving up when she received the encouraging call.

was 是 be 动词的过去式，表示"处于某种状态"。 at 是介词，表示"在...位置/状态"。 the 是定冠词，特指某个事物。 point 在这里指"时刻、阶段"。 of 是介词，表示所属关系。 was at the point of 是一个固定短语，意思是"正处于...的边缘/即将..."，表示某人即将做某事或处于某种状态的临界点。