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Chapter 2: Problem 21

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

Short Answer

Expert verified
The midpoint of the line segment with endpoints (-2,-8) and (-6,-2) is (-4,-5).

Step by step solution

01

Input line segment endpoints

The two endpoints of the line segment are (-2,-8) and (-6,-2). Therefore, the coordinates of these endpoints are A(-2,-8) and B(-6,-2). Let \(x1, y1)\) be the coordinates of A and \((x2, y2)\) those of B.
02

Apply the midpoint formula

The formula for finding the midpoint, M, of a line segment with endpoints A and B in two-dimensional space is: \(M = [(x1+x2)/2, (y1+y2)/2] \). The midpoint is the point directly halfway between the two given points, and its coordinates are the averages of the x and y coordinates of the points.
03

Compute the midpoint

Substitute the given coordinates into the formula: \(M = [(-2+-6)/2, (-8+-2)/2] = [-8/2, -10/2] = [-4, -5]\). So, the midpoint M is at (-4,-5).

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