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Chapter 2: Problem 24

Find the midpoint of each line segment with the given endpoints. $$(-2,-1) \text { and }(-8,6)$$

Short Answer

Expert verified
The midpoint of the line segment with endpoints (-2,-1) and (-8,6) is (-5, 2.5).

Step by step solution

01

Identify the coordinates of endpoints

The coordinates of the endpoints of the line segment are \((-2, -1)\) and \((-8, 6)\). Therefore, we have \(x_1 = -2\), \(y_1 = -1\), \(x_2 = -8\), and \(y_2 = 6\).
02

Apply the Midpoint Formula

The midpoint \((x_m, y_m)\) of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(((x_1+x_2)/2 , (y_1+y_2)/2)\). Substitute the given values into the formula to find the midpoint. So, \(x_m = (x_1+x_2)/2 = (-2-8)/2 = -5\) and \(y_m = (y_1+y_2)/2 = (-1+6)/2 = 2.5\)
03

Write Down the Midpoint

After calculating the values of \(x_m\) and \(y_m\), we find that the midpoint of the line segment with the given endpoints is \((-5, 2.5)\).

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