Each unit on a park map represents 1 meter. A slide is located at $(-85,-11)$. A set of swings is located at $(-21,-11)$. What is the distance between the slide and the swings in meters?
The locations of the slide and the swings are given by their coordinates on a Cartesian plane: the slide is at \(A = (-85, -11)\) and the swings are at \(B = (-21, -11)\). Since 1 unit on the map corresponds to 1 meter, we aim to find the distance between these two points in units, which directly translates to meters.
We observe that the y-coordinates of both the slide and the swings are identical, as both are at \(y = -11\). This means the segment connecting these two locations is a horizontal line segment. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_1)\) on a horizontal line is given by the absolute difference of their x-coordinates: \(d = |x_2 - x_1|\).
Using the coordinates \(x_1 = -85\) and \(x_2 = -21\), we substitute these into the distance formula:
\(d = |(-21) - (-85)|\)
\(d = |-21 + 85|\)
\(d = |64|\)
The distance is 64 units. Since 1 unit represents 1 meter, the distance is 64 meters.
Understanding how to calculate distances on a map using coordinates is essential for planning paths and navigating environments. For example, if you are designing a park, knowing the exact distance between play areas like the slide and the swings helps in determining the amount of pathway material needed or how long it will take for a child to walk between them. By using the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), you can easily calculate these distances, ensuring your park layout is both safe and well-planned.