Question

In the following exercise, find the distance between the points. Round to the nearest tenth if needed:

$\left(1,-4\right)$and$\left(5,-5\right)$

Short answer

4.1

Step-by-step solution

Step 1. Given information.

The coordinate of the two points are$\left(1,-4\right)$and$\left(5,-5\right)$.

Step 2. Finding the distance between the two points.

The distance between the points $\left(x_1,y_1\right)$and $\left(x_2,y_2\right)$can be expressed as

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

Substituting the coordinate of the points, the distance between the two given points will be

$$\begin{gathered} d=\sqrt{{\left(5-1\right)}^2+{\left(-5-\left(-4\right)\right)}^2} \\ d=\sqrt{4^2+{\left(-1\right)}^2} \\ d=\sqrt{17} \\ d=4.123 \end{gathered}$$

Rounding to the nearest tenth, the distance between the two points will be$d=4.1$