Geometry

The answer is A.

 

1. Recall the definition of a mid - point:

A mid - point of a line segment divides the segment into two equal parts. That is, if  is the mid - point of segment , then .

 

2. Analyze each figure:

First figure: The tick marks show that the distance from  to  is equal to the distance from  to . So,  divides segment  into two equal parts, and  is the mid - point of .

 

Second figure: The tick marks indicate that  and  are equal, which means  is the mid - point of , not  being the mid - point of

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