Chapter 11.6, Problem 6E

To determine

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

Answer to Problem 6E

  $d=5$ .

Explanation of Solution

Given:

The given points are $\left(7,-2\right),\left(4,-6\right)$ .

Calculation:

As the given pairs of point are $\left(7,-2\right),\left(4,-6\right)$ .

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

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(4-7\right)}^2+{\left(-6-\left(-2\right)\right)}^2}\left\{\text{substitutes the given value}\right\}\\ d=\sqrt{{\left(-3\right)}^2+{\left(-4\right)}^2}\left\{\text{simplify}\right\}\\ \therefore d=\sqrt{9+16}\{\because {\left(-4\right)}^2=16,{\left(-3\right)}^2=9\}\\ \Rightarrow d=\sqrt{25}\left\{\text{add the both terms}\right\}\\ \therefore d=\sqrt{5^2}\\ d=5\end{array}$

Hence, the distance between the given points to the nearest tenth is $d=5$ .