Midpoint Formula Question 5 of 10 2 Points What is the midpoint of the segment shown below? O A. (6,3) O B. (51,3) O c. (62.3) O ) 10 (2, 3) (10, 3) 10 10 D. (5, 3 10 SUBA
The Correct Answer and Explanation is :
To find the midpoint of a segment, we use the midpoint formula. The midpoint formula is:
[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
]
Where:
- ( (x_1, y_1) ) are the coordinates of the first endpoint,
- ( (x_2, y_2) ) are the coordinates of the second endpoint.
Step-by-step Explanation:
From the options provided, it seems there is a pair of coordinates for the endpoints, but they are a bit unclear. Let’s assume the segment has the endpoints ( (10, 3) ) and ( (0, 3) ). This assumption is based on the “10” and “3” appearing multiple times in the question. Let’s proceed with these points:
- The coordinates of the two endpoints are ( (10, 3) ) and ( (0, 3) ).
- First endpoint ( (x_1, y_1) = (10, 3) )
- Second endpoint ( (x_2, y_2) = (0, 3) )
- Apply the midpoint formula:
[
\text{Midpoint} = \left( \frac{10 + 0}{2}, \frac{3 + 3}{2} \right)
]
[
\text{Midpoint} = \left( \frac{10}{2}, \frac{6}{2} \right)
]
[
\text{Midpoint} = (5, 3)
]
Therefore, the correct midpoint of the segment is ( (5, 3) ).
Conclusion:
The correct answer is D. (5, 3).
Explanation:
The midpoint formula is a fundamental concept in geometry used to find the point exactly halfway between two points in a coordinate plane. It is important to remember that this formula works for both the x and y coordinates separately. By averaging the x-coordinates and y-coordinates of the endpoints, you can determine the midpoint, which divides the line segment into two equal parts. In this case, using the points ( (10, 3) ) and ( (0, 3) ), we found that the midpoint lies at ( (5, 3) ).