Question

define the condition of a line segment AB, such that point C is called the mid -point of AB

Answer 1

your question might be answered by coordinate geometry.........
let, the point "A" is expressed as the point (x1 , y1 ) and the point "B" is expressed as the point ( x2 , y2 )

If the point "C" is the mid point of the line segment AB , then the point "C" might be expressed as......

"C" =>
$( \frac{x1 + x2}{2} ,\frac{x2 + y2}{2} )$