Question

In the following ecercises,find the distance between the points.Write the answer in exact form and the find the decimal approximation,rounded the nearest tenth if needed.

$\left(-7,-3\right)$and$\left(8,5\right)$

Short answer

The distance$d=17$.

Step-by-step solution

Step 1.Given information

Consider the given points $\left(-7,-3\right)and\left(8,5\right)$.

The distance formula states that the distance $d$ between points $\left(x_1,y_1\right)and\left(x_2,y_2\right)$ is$d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Step 2.First lable the points.

$\left(x_1,y_1\right)=\left(-7,-3\right)and\left(x_2,y_2\right)=\left(8,5\right)$.

Now substitute $x_1,x_{2,}{y}_{1}and{y}_2$values in the distance formula.

$d=\sqrt{{\left(8-(-7\right)}^2+{\left(5-(-3\right)}^2}$

Step 3.Now simplify the radical as shown as below

$$\begin{gathered} d=\sqrt{{\left(8+7\right)}^2+{\left(5+3\right)}^2} \\ =\sqrt{{\left(15\right)}^2+{\left(8\right)}^2} \\ =\sqrt{225+64} \\ =\sqrt{289} \\ =17 \end{gathered}$$

Therefore,the distance islocalid="1645194269623" $d=17$