Chapter SH, Problem 14PTDF

Solution

The distance between the points $\left(-2,9\right),\text{ and }\left(0,0\right)$ .

  $9.2\text{ units}$

Given:

The pair of points, $\left(-2,9\right),\text{ and }\left(0,0\right)$ .

Concept Used:

Distance between the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula,

  $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$ .

Calculation:

In order to find the distance between the points $\left(-2,9\right),\text{ and }\left(0,0\right)$ , substitute the value of the points into the distance formula and simplify further as shown below

  $\begin{array}{c}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(0-\left(-2\right)\right)}^2+{\left(0-9\right)}^2}\\ =\sqrt{{\left(0+2\right)}^2+{\left(-9\right)}^2}\\ =\sqrt{4+81}\\ =\sqrt{85}\\ =9.219\\ \approx 9.2\end{array}$

Thus, the distance between the points is about $9.2\text{ units}$ .