Question

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

$(1,-4)$and$(6,8)$

Short answer

The distance is $13$.

Step-by-step solution

Step 1. Given Information

We are given points $(1,-4),(6,8)$.

The distance formula states that the distance 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. Applying the formula

Consider the point $(1,-4)$as $\left(x_1,y_1\right)$and $(6,8)$as $\left(x_2,y_2\right)$.

Substituting the values in the distance formula, we get

$$\begin{gathered} d=\sqrt{(6-1{)}^2+[8-(-4){]}^2} \\ d=\sqrt{(5{)}^2+[8+4{]}^2} \\ d=\sqrt{(5{)}^2+{\left(12\right)}^2} \\ d=\sqrt{25+144} \\ d=\sqrt{169} \\ d=13 \end{gathered}$$