Question

question 2 of 10
a line segment may have more than one midpoint.
a. true
b. false

Explanation:

Step1: Define mid - point

A mid - point of a line segment divides it into two equal parts.

Step2: Prove uniqueness

Suppose there are two points \(M_1\) and \(M_2\) as mid - points of a line segment \(AB\). Let the coordinates of \(A=(x_1,y_1)\), \(B=(x_2,y_2)\). The mid - point formula gives the coordinates of the mid - point \(M\) as \(M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). If \(M_1\) and \(M_2\) are mid - points, then they must coincide because there is only one way to divide a line segment into two equal parts. So a line segment has exactly one mid - point.

Answer:

B. False