- Identify that the school at \((4, -30)\) and the park at \((4, -10)\) share the same x-coordinate.
- Recognize that the distance between these points is the absolute difference of their y-coordinates.
- Calculate the distance as \(|-10 - (-30)| = 20\) units.
- The distance from the school to the park is \(\boxed{20}\) units.
Explanation
- Analyze the coordinates of the two locations.
The locations of the school and the park are given as coordinate points on a plane. The school is at \(S = (4, -30)\) and the park is at \(P = (4, -10)\). To determine the distance between these two locations, we examine their coordinates. We notice that both points have the same x-coordinate, which is \(x = 4\). This indicates that the points lie on a vertical line.
- Calculate the distance between the points.
Since the school and the park lie on the same vertical line, the distance between them is the absolute difference between their y-coordinates. The y-coordinate of the park is \(y_2 = -10\) and the y-coordinate of the school is \(y_1 = -30\). The formula for the distance \(d\) between two points \((x, y_1)\) and \((x, y_2)\) is given by:
\[d = |y_2 - y_1|\]
Substituting the known values into this formula:
\[d = |(-10) - (-30)|\]
\[d = |-10 + 30|\]
\[d = |20|\]
\[d = 20\]
Therefore, the distance between the school and the park is 20 units.
Examples
If you are looking at a city map on a grid, understanding distances between specific points like schools, parks, or stores can help you estimate travel time or choose the most efficient path. For example, if you are planning a bike ride and know the coordinates of your home and a friend's house, you can quickly calculate the distance to see how long your trip will be. In this case, the vertical distance of 20 units helps you understand how far apart these two locations are in the city.