Given the line segment AR
The coordinate of A is 0.
AR=10
First, we determine the coordinate of R.
[tex]\begin{gathered} |A-R|=10 \\ |0-R|=10 \\ |-R|=10 \\ R=10 \end{gathered}[/tex]Therefore, the coordinate of R is 10(to the right of A
) or -10(to the left of A).
The midpoint of a number line is calculated using the formula below:
[tex]\begin{gathered} \text{Midpoint}=\frac{x_2+x_1}{2} \\ \text{where }x_{2\; }and\; x_1are\text{ the endpoints of the line.} \end{gathered}[/tex]Therefore, the only possible coordinate for the midpoint of the segment AR is:
[tex]\text{Midpoint}=\frac{0+10}{2}=5[/tex]Therefore:
• If R is to the left of A, the midpoint of AR = -5
,• If R is to the right of A, the midpoint of AR = 5
The possible coordinates for the midpoint of the segment AR are 5 and -5.