Find the midpoint, M, of \overline{AB}.\newline A\newline 0\newline M\newline [?]\newline B\newline 26
The Correct Answer and Explanation is:
To find the midpoint MMM of a line segment AB‾\overline{AB}AB, we use the midpoint formula. The midpoint MMM is the point that divides the segment AB‾\overline{AB}AB into two equal parts. The formula for the midpoint of a segment with endpoints at A(x1)A(x_1)A(x1) and B(x2)B(x_2)B(x2) on a number line is: M=x1+x22M = \frac{x_1 + x_2}{2}M=2×1+x2
Step-by-Step Solution:
You are given that A=0A = 0A=0 and B=26B = 26B=26, and we need to find the midpoint MMM.
- Substitute the values of AAA and BBB into the midpoint formula:
M=0+262M = \frac{0 + 26}{2}M=20+26
- Add the values inside the parentheses:
M=262M = \frac{26}{2}M=226
- Divide the result:
M=13M = 13M=13
So, the midpoint MMM is 13.
Explanation:
The midpoint of a line segment is essentially the average of the two endpoints. In this case, we are given that AAA is at position 0 on the number line and BBB is at position 26. The midpoint is calculated by averaging these two positions. The result is 131313, meaning that MMM lies exactly halfway between AAA and BBB.
This concept can be visualized as dividing the segment into two equal lengths. From A=0A = 0A=0 to M=13M = 13M=13, and from M=13M = 13M=13 to B=26B = 26B=26, the distances are both 13 units, confirming that MMM is indeed the midpoint.
In conclusion, the midpoint of AB‾\overline{AB}AB where A=0A = 0A=0 and B=26B = 26B=26 is M=13M = 13M=13.
