Chapter 11.6, Problem 4E

To determine

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

Answer to Problem 4E

  $d=15.23$ .

Explanation of Solution

Given:

The given points are $\left(10,3\right),\left(-4,9\right)$ .

Calculation:

As the given pairs of point are $\left(10,3\right),\left(-4,9\right)$ .

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

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(-4-10\right)}^2+{\left(9-3\right)}^2}\left\{\text{substitutes the given value}\right\}\\ d=\sqrt{{\left(-14\right)}^2+{\left(6\right)}^2}\left\{\text{simplify}\right\}\\ \therefore d=\sqrt{196+36}\{\because 6^2=36,{\left(-14\right)}^2=196\}\\ \Rightarrow d=\sqrt{232}\left\{\text{add the both terms}\right\}\\ \therefore d=15.2315\\ d=15.23\left\{\text{round up to nearest tenth}\right\}\end{array}$

Hence, the distance between the given points to the nearest tenth is $d=15.23$ .