Question
Question 1 (2 points) A midpoint of a segment is the point that divides the segment into two congruent segments. The midpoint of \( \overline{P Q} \) with \( P\left(x_{1}, y_{1}\right) \) and \( Q\left(x_{2}, y_{2}\right) \), is: \( M=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right) \) True False
Ask by Rowe Hart. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The midpoint \( M \) of segment \( \overline{PQ} \) is \( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).
Solution
**True**
The midpoint \( M \) of the segment \( \overline{PQ} \) with endpoints \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is correctly given by:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
This formula accurately calculates the coordinates that equally divide the segment into two congruent parts.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
True! The formula provided accurately represents how to calculate the midpoint of a segment with endpoints \( P \) and \( Q \). By averaging the x-coordinates and y-coordinates of both points, you'll find the exact middle point, ensuring each section is equal in length. This concept is not just a mathematical idea; it comes in handy in various real-world situations, like construction and design, where finding the center point of a space is crucial. It can also help in navigation, ensuring that routes and paths between two locations are balanced and efficient!
