Chapter 11.6, Problem 3E

To determine

To find: the distance between the given points to the nearest tenth.

Answer to Problem 3E

  $d=6.70$ .

Explanation of Solution

Given:

The given points are $\left(3,4\right),\left(9,7\right)$ .

Calculation:

As the given pairs of point are $\left(3,4\right),\left(9,7\right)$ .

Since, the distance formula is $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$ .

Therefore, the distance between the given points is

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(9-3\right)}^2+{\left(7-4\right)}^2}\left\{\text{substitutes the given value}\right\}\\ d=\sqrt{{\left(6\right)}^2+{\left(3\right)}^2}\left\{\text{simplify}\right\}\\ \therefore d=\sqrt{36+9}\{\because 6^2=36,3^2=9\}\\ \Rightarrow d=\sqrt{45}\left\{\text{add the both terms}\right\}\\ \therefore d=6.7082\\ d=6.70\left\{\text{round up to nearest tenth}\right\}\end{array}$

Hence, the distance between the given points to the nearest tenth is $d=6.70$ .