The coordinate plane (intro)
The idea
A treasure map that says walk 3 steps east and 5 steps north is using the same idea as the coordinate plane. The plane is a grid built from two number lines: one running to the right and one running up, meeting at a starting corner where both read 0. Any spot on the grid gets an address made of two numbers in parentheses, like (3, 5): the first number says how many steps to go right from the corner, and the second says how many steps to go up.
The order of the two numbers is a promise that everyone keeps: right first, then up. Break the promise and you land in the wrong place — (2, 6) means 2 right and 6 up, while (6, 2) means 6 right and 2 up, two genuinely different spots. So the most common error is simply swapping the pair. A good habit is to trace the path with a finger every time: start at the corner, slide right along the bottom, then climb straight up, and say the moves out loud as you go.
Worked example
On a park map, each grid step is 1 meter. The slide stands at the point (2, 1) and the water fountain stands at (2, 6). Describe where each one sits on the grid, then find the length of the straight walk from the slide to the fountain.
- Read each address the same way: first number is steps right from the corner of the map, second number is steps up. The slide sits 2 right and 1 up; the fountain sits 2 right and 6 up.
- Both points are exactly 2 steps right, so they stand on the same straight up-and-down grid line. Walking between them changes only the up direction.
- Count the climb from 1 up to 6 up: 6 − 1 = 5 grid steps, and each step on this map is 1 meter.
- So the straight walk is 5 meters. Note that (2, 6) is not the same spot as (6, 2) — swapping the numbers would send you somewhere else entirely.
Answer. The walk from the slide to the fountain is 5 meters, straight up the map.
Check your understanding
- Why do the two numbers in a point need a fixed order, like the parts of a street address?
- What routes do (3, 5) and (5, 3) each describe, and why do they end at different spots?
- How is naming a point on a grid like finding your seat in a movie theater?
- When two points share their first number, what does the picture look like, and how would you find the distance between them?