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.

$(-1,4)$and$\left(2,0\right)$.

Short answer

The distance is$d=5.$

Step-by-step solution

Step 1.Given information

Consider the given points $\left(-1,4\right)$and $\left(2,0\right)$

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 

$\left(x_1,y_1\right)=\left(-1,4\right)and\left(x_2,y_2\right)=\left(2,0\right)$.

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

$d=\sqrt{{\left(2-(-1\right)}^2+{(0-4)}^2}$

Step 3.Now simplify the radical as shown as below

$$\begin{gathered} d=\sqrt{{\left(2+1\right)}^2+{\left(-4\right)}^2} \\ =\sqrt{3^2+{(-4)}^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}$$

Therefore,the distance$d=5$