Q59. - Algebra 1

Question

How far apart in feet are the swings from the slide?

Step-by-Step Solution

Answer

The swings are 4.1 feet apart from the slide.

Step 1. Given.

The graph is given.

Step 2. Write the distance formula to find the distance between the given two points.

The distance (d) between the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by:

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

Step 3. Determine how far apart are the swings from the slide.

From the given graph, it can be noticed that the coordinates of the location of swings and slide are $\left(1,9\right)$ and $\left(2,5\right)$ respectively.

Therefore, the distance (d) between the points $\left(1,9\right)$ and $\left(2,5\right)$ is:

$$\begin{gathered} d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2} \\ =\sqrt{{\left(2-1\right)}^2+{\left(5-9\right)}^2} \\ =\sqrt{{\left(1\right)}^2+{\left(-4\right)}^2} \\ =\sqrt{1+16} \\ =\sqrt{17} \\ =4.1231056 \\ \approx 4.1 \end{gathered}$$

Therefore, the swings are 4.1 feet apart from the slide.