Question
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Find the midpoint of the line segment with the given endpoints. \[ (-2,-5) \text { and }(-4,-2) \] The midpoint is \( \square \). (Type an ordered pair.)

Ask by Brewer Adkins. in the United States
Dec 11,2024

Real Tutor Solution

Tutor-Verified Answer

Answer

The midpoint is \((-3, -\frac{7}{2})\).

Solution

To find the midpoint of a line segment with endpoints \((-2, -5)\) and \((-4, -2)\), we use the midpoint formula: \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Here, \((x_1, y_1) = (-2, -5)\) and \((x_2, y_2) = (-4, -2)\). Now, we can calculate the midpoint: 1. Calculate the x-coordinate of the midpoint: \[ \frac{-2 + (-4)}{2} = \frac{-2 - 4}{2} = \frac{-6}{2} = -3 \] 2. Calculate the y-coordinate of the midpoint: \[ \frac{-5 + (-2)}{2} = \frac{-5 - 2}{2} = \frac{-7}{2} = -\frac{7}{2} \] Putting it all together, the midpoint is: \[ \left(-3, -\frac{7}{2}\right) \] Thus, the midpoint is \(\boxed{(-3, -\frac{7}{2})}\).

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The Deep Dive

To find the midpoint of a line segment with endpoints \((-2, -5)\) and \((-4, -2)\), use the midpoint formula: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Plugging in the values: \[ \left( \frac{-2 + (-4)}{2}, \frac{-5 + (-2)}{2} \right) = \left( \frac{-6}{2}, \frac{-7}{2} \right) = \left( -3, -\frac{7}{2} \right) \] Thus, the midpoint is \((-3, -\frac{7}{2})\).

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