5. In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
AC=BC ... (i) If possible, let D be another mid-point of AB. AD=DB ... (ii) Subtracting (ii) from (i) AC–AD=BC–DB DC=−DC (∵AC−AD=DCandCB−DB=−DC) DC+DC=0 2DC=0 DC=0 So, C and D coincide. Thus, every line segment has one and only one mid-point.
