Chapter 9.1, Problem 2WE

To determine

To calculate: The distance between the pairs of points.

Answer to Problem 2WE

The distance between the given points is 10.

Explanation of Solution

Given information: The coordinates of points are $\left(0,8\right)$ and $\left(-6,0\right)$ .

Formula used: $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Calculation: Apply the distance formula to calculate the distance between the two points.

  $\begin{array}{cc}A& B\\ x_1=0& x_2=-6\\ y_1=8& y_2=0\end{array}$

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(-6-0\right)}^2+{\left(0-8\right)}^2}\\ d=\sqrt{36+64}\\ d=\sqrt{100}\\ d=10\end{array}$

Therefore, the required distance between the points is 10.

To determine

To calculate: The midpoint of line segment.

Answer to Problem 2WE

The coordinates of the midpoint of the line segment are $\left(-3,4\right)$ .

Explanation of Solution

Given information: The coordinates of points are $\left(0,8\right)$ and $\left(-6,0\right)$ .

Formula used: $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Calculation: Since the line segment joining the given points, consider point M as a midpoint.

  $\begin{array}{cc}A& B\\ x_1=0& x_2=-6\\ y_1=8& y_2=0\end{array}$

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{0-6}{2},\frac{8+0}{2}\right)\\ M=\left(-3,4\right)\end{array}$

Hence, the coordinates of the midpoint of the line segment are $\left(-3,4\right)$ .