Can Someone help me with this geometry question?

Question

This is the entire question.

 

What theorem is contradicted if an indirect proof leads to this situation:

 

"Point M and point N are both midpoints of line segment"

 

Thanks!

Answer 1

Hi Hayley,

 

Mark is correct about a line having only one midpoint.

 

The Midpoint Theorem states that the coordinates of the midpoint are the average of the x coordinates of the 2 endpoints and the average of the y coordinates of the endpoints.

 

Therefore, to have more than one midpoint on a line would be a violation of the Midpoint Theorem.

 

God bless, Jordan.