What is the midpoint of FB? A F G H L -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 B point A point G point H point L
The Correct Answer and Explanation is:
To find the midpoint of line segment FB, we need the coordinates of points F and B from the given number line:
From the number line:
- F is located at -9
- B is located at 9
Step-by-Step Solution:
Step 1: Use the midpoint formula
The formula for the midpoint MM between two points x1x_1 and x2x_2 on a number line is: M=x1+x22M = \frac{x_1 + x_2}{2}
Step 2: Plug in the coordinates
M=−9+92=02=0M = \frac{-9 + 9}{2} = \frac{0}{2} = 0
So, the midpoint of FB is 0.
Explanation
The concept of a midpoint is foundational in both geometry and algebra. It refers to the point that lies exactly halfway between two other points on a number line or coordinate plane. In this problem, you are given a horizontal number line that ranges from -9 to 9, with several labeled points, including F at -9 and B at 9.
To determine the midpoint of segment FB, we apply the midpoint formula for a number line: Midpoint=x1+x22\text{Midpoint} = \frac{x_1 + x_2}{2}
This formula adds the two endpoints and divides the sum by 2 to find the average location between them. In this case, point F is at -9 and point B is at 9. Substituting into the formula: −9+92=02=0\frac{-9 + 9}{2} = \frac{0}{2} = 0
Thus, the midpoint is at 0, which means it lies right at the center of the number line.
Understanding midpoints is useful in many real-life applications, such as construction, mapping, and computer graphics, where precise central positioning is essential. It also helps in understanding symmetry and balance in both physical and mathematical contexts.
In this example, since F and B are on opposite ends of a symmetric number line, the midpoint logically falls at 0—the exact center. No matter how far apart the points are, the midpoint formula gives a consistent method to find the halfway mark. Therefore, the midpoint of segment FB is 0.
