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.

$(-1,3)$and$\left(5,-5\right)$

Short answer

The distance is$d=10$

Step-by-step solution

Step 1.Given information

Consider the given points $\left(-1,3\right)and(5,-5)$

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 as

$\left(x_1,y_1\right)=\left(-1,3\right)and\left(x_2,y_2\right)=\left(5,-5\right)$.

Now substitute $x_1,y_1,x_{2}and{y}_2$values in the distance formula.

localid="1667916127572" $d=\sqrt{(5-{(-1))}^2+{\left(-5-3\right)}^2}$

Step 3.Now simplify the radical as shown as below

$$\begin{gathered} d=\sqrt{{\left(6\right)}^2+(-8}{)}^2 \\ =\sqrt{36+64} \\ =\sqrt{100} \\ =10 \end{gathered}$$

Therefore the distance$d=10$