Question
\( \overline{S T} \) has endpoints at \( S(8,-18) \) and \( T(-10,20) \). Find the midpoint \( M \) of \( \overline{S T} \). Write the coordinates as decimals or integers. \( M=(\square, \square) \) Submit
Ask by Johnston Chambers. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The midpoint \( M \) is at \( (-1, 1) \).
Solution
To find the midpoint, use the midpoint formula:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
For S(8, -18) and T(-10, 20):
x-coordinate: (8 + (-10)) / 2 = (-2) / 2 = -1
y-coordinate: (-18 + 20) / 2 = (2) / 2 = 1
Thus, the midpoint M = (-1, 1).
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Simplify this solution Mind Expander
To find the midpoint \( M \) of the line segment \( \overline{S T} \) with endpoints \( S(8,-18) \) and \( T(-10,20) \), you can use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Where \( (x_1, y_1) = S(8, -18) \) and \( (x_2, y_2) = T(-10, 20) \): Calculating the x-coordinate of \( M \): \[ \frac{8 + (-10)}{2} = \frac{8 - 10}{2} = \frac{-2}{2} = -1 \] Calculating the y-coordinate of \( M \): \[ \frac{-18 + 20}{2} = \frac{-18 + 20}{2} = \frac{2}{2} = 1 \] Thus, the coordinates of the midpoint \( M \) are: \[ M = (-1, 1) \] So, the final answer is \( M=(-1, 1) \).
