Question
\( \overline{T U} \) has endpoints at \( T(0,2) \) and \( U(2,7) \). Find the mid Write the coordinates as decimals or integers. \[ M=(\square) \]
Ask by Johnston Mcdonald. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The midpoint \( M \) is at \( (1, 4.5) \).
Solution
To find the midpoint \( M \) of the line segment with endpoints \( T(0, 2) \) and \( U(2, 7) \), we use the midpoint formula:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Plugging in the coordinates of \( T \) and \( U \):
\[
M = \left( \frac{0 + 2}{2}, \frac{2 + 7}{2} \right) = \left( \frac{2}{2}, \frac{9}{2} \right) = (1, 4.5)
\]
**Answer:**
\[ M = (1,\ 4.5) \]
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Simplify this solution Bonus Knowledge
To find the midpoint \( M \) of the line segment \( \overline{TU} \), we use the midpoint formula, which is given by \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Here, the coordinates of point \( T \) are \( (x_1, y_1) = (0, 2) \) and the coordinates of point \( U \) are \( (x_2, y_2) = (2, 7) \). Substituting in the values: \[ M = \left( \frac{0 + 2}{2}, \frac{2 + 7}{2} \right) = \left( \frac{2}{2}, \frac{9}{2} \right) = (1, 4.5) \] So, the coordinates of the midpoint \( M \) are: \[ M = (1, 4.5) \]
