Question
\( U(9,2) \) and \( V(20,6) \) are the endpoints of a line segment. What is the midpoint \( M \) of that line segment? Write the coordinates as decimals or integers. \( \quad M=(\square \)
Ask by Mejia Brewer. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( M = (14.5,\ 4) \)
Solution
To find the midpoint \( M \) of the line segment with endpoints \( U(9,2) \) and \( V(20,6) \), you can use the midpoint formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Substituting the given coordinates:
\[
M = \left( \frac{9 + 20}{2}, \frac{2 + 6}{2} \right) = \left( \frac{29}{2}, \frac{8}{2} \right) = (14.5, 4)
\]
**Answer:** \( M = (14.5,\ 4) \)
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Simplify this solution Beyond the Answer
To find the midpoint \( M \) of the line segment defined by the endpoints \( U(9,2) \) and \( V(20,6) \), we use the midpoint formula: \[ M\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right) \] Substituting the coordinates of points \( U \) and \( V \): \[ M\left( \frac{9+20}{2}, \frac{2+6}{2} \right) = M\left( \frac{29}{2}, \frac{8}{2} \right) = M(14.5, 4) \] So, the coordinates of the midpoint \( M \) are \( M=(14.5, 4) \).
