Chapter 9.1, Problem 9WE

To determine

To calculate: The distance between the pairs of points.

Answer to Problem 9WE

The distance between the given points is $15.56$ .

Explanation of Solution

Given information: The coordinates of points are $\left(0,0\right)$ and $\left(11,11\right)$ .

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.

  $\begin{array}{cc}A& B\\ x_1=0& x_2=11\\ y_1=0& y_2=11\end{array}$

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(11-0\right)}^2+{\left(11-0\right)}^2}\\ d=\sqrt{121+121}\\ d=\sqrt{242}\\ d=15.56\end{array}$

Therefore, the required distance between the points is $15.56$ .

To determine

To calculate: The midpoint of line segment.

Answer to Problem 9WE

The coordinates of the midpoint of the line segment are $\left(5.5,5.5\right)$ .

Explanation of Solution

Given information: The coordinates of points are $\left(0,0\right)$ and $\left(11,11\right)$ .

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.

  $\begin{array}{cc}A& B\\ x_1=0& x_2=11\\ y_1=0& y_2=11\end{array}$

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{0+11}{2},\frac{0+11}{2}\right)\\ M=\left(\frac{11}{2},\frac{11}{2}\right)\\ M=\left(5.5,5.5\right)\end{array}$

Hence, the coordinates of the midpoint of the line segment are $\left(5.5,5.5\right)$ .