Pregunta
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
Solución de tutoría real
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The midpoint \( M \) of segment \( \overline{PQ} \) is \( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).
Solución
**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.
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Simplifique esta solución 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!
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