Chapter 9.1, Problem 1WE

To determine

To calculate: The distance between the pairs of points.

Answer to Problem 1WE

The distance between the given points is 13.

Explanation of Solution

Given information: The coordinates of points are $\left(13,6\right)$ and $\left(0,6\right)$ .

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.

  $\begin{array}{cc}A& B\\ x_1=13& x_2=0\\ y_1=6& y_2=6\end{array}$

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(0-13\right)}^2+{\left(6-6\right)}^2}\\ d=\sqrt{169}\\ d=13\end{array}$

Therefore, the required distance between the points is 13.

To determine

To calculate: The midpoint of line segment.

Answer to Problem 1WE

The coordinate of the midpoint of the line segment is $\left(\frac{13}{2},6\right)$ .

Explanation of Solution

Given information: The coordinates of points are $\left(13,6\right)$ and $\left(0,6\right)$ .

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.

  $\begin{array}{cc}A& B\\ x_1=13& x_2=0\\ y_1=6& y_2=6\end{array}$

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{13+0}{2},\frac{6+6}{2}\right)\\ M=\left(\frac{13}{2},6\right)\end{array}$

Hence, the coordinate of the midpoint of the line segment is $\left(\frac{13}{2},6\right)$ .