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Chapter 2: Problem 26

Find the midpoint of each line segment with the given endpoints. $$\left(-\frac{2}{5}, \frac{7}{15}\right) \text { and }\left(-\frac{2}{5},-\frac{4}{15}\right)$$

Short Answer

Expert verified
The midpoint of the line segment with the given endpoints is \(-\frac{2}{5}, \frac{1}{5}\)

Step by step solution

01

Identify the coordinates of the endpoints

The given endpoints are \(\left(-\frac{2}{5}, \frac{7}{15}\right)\) and \(\left(-\frac{2}{5},-\frac{4}{15}\right)\). So, \(x_1 = -\frac{2}{5}\), \(y_1 = \frac{7}{15}\), \(x_2 = -\frac{2}{5}\) and \(y_2 = -\frac{4}{15}\).
02

Calculate the x-coordinate of the midpoint

Using the formula for the x-coordinate of the midpoint, we have: \(x_m = \frac{x_1 + x_2}{2} = \frac{-\frac{2}{5} + -\frac{2}{5}}{2} = -\frac{2}{5}\).
03

Calculate the y-coordinate of the midpoint

Using the formula for the y-coordinate of the midpoint, we get: \(y_m = \frac{y_1 + y_2}{2} = \frac{\frac{7}{15} + -\frac{4}{15}}{2} = \frac{1}{5}\).
04

Present the midpoint

The midpoint of the line segment with the given endpoints is thus \(-\frac{2}{5}, \frac{1}{5}\)

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If you know a point on a line and you know the equation of a line perpendicular to this line, explain how to write the line's equation.

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