Interpret a Local Coordinate Model
Read signed fictional coordinates and keep the model distinct from latitude and longitude.
Supplied materials
- Original fictional local grid: library is origin (0,0); first coordinate x counts blocks east if positive and west if negative; second y counts blocks north if positive and south if negative. Studio (3,2), garden (-2,1), clinic (3,-1). One block is 100 m along a grid edge. These invented local coordinates are not latitude and longitude.
Learn the idea
Coordinates locate points within a stated system. Here (3,2) means three blocks east and two north of the library. The sign matters: a negative x points west, while a negative y points south. Start with the system’s definitions before plotting; an unfamiliar pair of numbers cannot identify a real place without a coordinate reference.
Positions and route distances answer different questions. The studio and clinic share x=3, so they lie on the same north-south grid line in this model. Their y values differ by three blocks, giving a 300 m vertical separation. This is a model calculation; it does not describe street names, safe paths, or the curved surface of Earth.
- Draw axes, mark their positive directions, and label the origin.
- Plot all three supplied points.
- Compare the studio and clinic’s x values and subtract their y values.
- State the vertical separation with units and name the coordinate system.
See the method in action
“Studio (3,2) and clinic (3,-1) have the same x. Their vertical separation is 2 − (−1) = 3 blocks, or 300 m. The garden at (-2,1) is two blocks west and one north of the library.”
Check your reasoning
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See the answer and explanation
Two blocks west and one north.
The local system defines negative x as west and positive y as north. It is expressly not a geographic latitude/longitude system.
Take it further
Changed model: each block is 250 m. What is the studio–clinic vertical separation now? Model reasoning: “The coordinate difference stays three blocks, but 3 × 250 = 750 m. The distance rule changes while the locations in block coordinates do not.”
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