Chapter 11.6, Problem 8E

To determine

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

Answer to Problem 8E

  $d=13$ .

Explanation of Solution

Given:

The given points are $\left(-4,7\right),\left(-9,-5\right)$ .

Calculation:

As the given pairs of point are $\left(-4,7\right),\left(-9,-5\right)$ .

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

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(-9-\left(-4\right)\right)}^2+{\left(-5-7\right)}^2}\left\{\text{substitutes the given value}\right\}\\ d=\sqrt{{\left(-5\right)}^2+{\left(-12\right)}^2}\left\{\text{simplify}\right\}\\ \therefore d=\sqrt{25+144}\{\because {\left(-5\right)}^2=25,{\left(-12\right)}^2=144\}\\ \Rightarrow d=\sqrt{169}\left\{\text{add the both terms}\right\}\\ \therefore d=13\end{array}$

Hence, the distance between the given points to the nearest tenth is $d=13$ .