Chapter 1, Problem 5RE

To determine

To plot: The given points and then find the distance and the mid points between the points.

Answer to Problem 5RE

The distance between the points are $3\sqrt{17}$ and the midpoints of the line joining the points is $\left(1,\frac{3}{2}\right)$ .

Explanation of Solution

Given:

The points are given as:

  $\left(-2,6\right)\text{and }\left(4,-3\right)$

Now plotting the points (-2,6) and drawing the line perpendicular to the each axis from the given points as shown below:

  

Similarly plotting the other point (4,-3):

  

Now, the distance between these two points:

  $\begin{array}{c}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(-3-6\right)}^2+{\left(4+2\right)}^2}\\ =\sqrt{{\left(-9\right)}^2+6^2}\\ =\sqrt{117}\\ =3\sqrt{17}\end{array}$

Now, the midpoints of the line joining the two point:

  $\begin{array}{c}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{-2+4}{2},\frac{6-3}{2}\right)\\ =\left(\frac{2}{2},\frac{3}{2}\right)\\ =\left(1,\frac{3}{2}\right)\end{array}$