Chapter P.2, Problem 18E

Solution

The distance between given two points.

7

Given information:

Given points are $\left(0,-8\right),\text{ and }\left(0,-1\right)$ .

Formula used:

The distance between two pints, $\left(x_1,y{1}_{}\right),\text{ and }\left(x_2,y{2}_{}\right)$ , is given by:

  $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y{2}_{}-y{1}_{}\right)}^2}$

Calculation:

To calculate the distance between $\left(0,-8\right),\text{ and }\left(0,-1\right)$ , use the formula for the distance between two points $\left(x_1,y{1}_{}\right),\text{ and }\left(x_2,y{2}_{}\right)$ that is

  $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y{2}_{}-y{1}_{}\right)}^2}$

Here, points are $\left(0,-8\right),\text{ and }\left(0,-1\right)$ , thus the distance is calculated as:

  $\begin{array}{c}\sqrt{{\left(0-0\right)}^2+{\left(-1-\left(-8\right)\right)}^2}=\sqrt{0^2+{\left(-1+8\right)}^2}\\ =\sqrt{0+7^2}\\ =\sqrt{49}\\ =7\end{array}$

Thus, the distance between the given two points is 7.