Question
Question 1 (1 point) \( \begin{array}{ll}\text { 11) }(-10,-7),(-8,1) & \text { 12) }(-6,-10),(-2,-10) \\ \text { Find the midpoint }\end{array} \)
Ask by Vaughn Powell. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The midpoints are \((-9,\ -3)\) for the first pair and \((-4,\ -10)\) for the second pair.
Solution
To find the midpoint between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the midpoint formula:
\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
**11) Points \((-10, -7)\) and \((-8, 1)\):**
\[
\text{Midpoint} = \left( \frac{-10 + (-8)}{2}, \frac{-7 + 1}{2} \right) = \left( \frac{-18}{2}, \frac{-6}{2} \right) = (-9, -3)
\]
**12) Points \((-6, -10)\) and \((-2, -10)\):**
\[
\text{Midpoint} = \left( \frac{-6 + (-2)}{2}, \frac{-10 + (-10)}{2} \right) = \left( \frac{-8}{2}, \frac{-20}{2} \right) = (-4, -10)
\]
**Final Answers:**
11) \((-9,\ -3)\)
12) \((-4,\ -10)\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the midpoint of the points \((-10, -7)\) and \((-8, 1)\), you can use the midpoint formula, which is \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right). \] Plugging in the values: \[ \left( \frac{-10 + (-8)}{2}, \frac{-7 + 1}{2} \right) = \left( \frac{-18}{2}, \frac{-6}{2} \right) = (-9, -3). \] For the points \((-6, -10)\) and \((-2, -10)\), applying the midpoint formula gives us: \[ \left( \frac{-6 + (-2)}{2}, \frac{-10 + (-10)}{2} \right) = \left( \frac{-8}{2}, \frac{-20}{2} \right) = (-4, -10). \] So, the midpoints are \((-9, -3)\) and \((-4, -10)\).
