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Chapter 32: Problem 1026

Determine the coordinates of the midpoint of the line segment joining the points \((3,-8)\) and \((-7,5)\).

Short Answer

Expert verified
The midpoint of the line segment joining the points $(3,-8)$ and $(-7,5)$ is $(-2, -\frac{3}{2})$.

Step by step solution

01

Identify the coordinates of the endpoints

Given the points \((3, -8)\) and \((-7, 5)\). We denote the first point as \((x_1, y_1) = (3, -8)\) and the second point as \((x_2, y_2) = (-7, 5)\).
02

Apply the midpoint formula

Now, we apply the midpoint formula: M = \(\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\) M = \(\left(\frac{3 + (-7)}{2}, \frac{-8 + 5}{2}\right)\)
03

Calculate the coordinates

Perform the calculations to find the coordinates of the midpoint M: M = \(\left(\frac{-4}{2}, \frac{-3}{2}\right)\) M = \((-2, -\frac{3}{2})\) So, the coordinates of the midpoint of the line segment joining the points \((3,-8)\) and \((-7,5)\) are \((-2, -\frac{3}{2})\).

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