Chapter P.2, Problem 28E

Solution

The midpoint of the line with the given end points.

  $\left(2,-1\right)$

Given information:

Given points are $\left(5,2\right),\text{ and }\left(-1,-4\right)$ .

Formula used:

The midpoint of a line segment with the end points $\left(x_1,y{1}_{}\right),\text{ and }\left(x_2,y{2}_{}\right)$ , is given by:

  $\left(\frac{x_2+x_1}{2},\frac{y{2}_{}+y{1}_{}}{2}\right)$

Calculation:

To calculate midpoint of the line with the given end points, use the formula for the midpoint of line segment with endpoints $\left(x_1,y{1}_{}\right),\text{ and }\left(x_2,y{2}_{}\right)$ that is

  $\left(\frac{x_2+x_1}{2},\frac{y{2}_{}+y{1}_{}}{2}\right)$

Here, points are $\left(5,2\right),\text{ and }\left(-1,-4\right)$ , thus the midpoint is calculated as:

  $\begin{array}{c}\left(\frac{5+\left(-1\right)}{2},\frac{2+\left(-4\right)}{2}\right)=\left(\frac{5-1}{2},\frac{2-4}{2}\right)\\ =\left(\frac{4}{2},\frac{-2}{2}\right)\\ =\left(2,-1\right)\end{array}$

Thus, the midpoint of the line segment with given end points is $\left(2,-1\right)$ .