You have placed numbers on a number line. Put two number lines together, one across and one up, crossing at 0, and every point on a flat grid gets its own address. That is the coordinate plane.
Idea clave
An ordered pair $(x, y)$ tells you how to reach a point from the origin $(0, 0)$: go $x$ units across along the x-axis, then $y$ units up. The order matters: $(2, 5)$ and $(5, 2)$ are different points.
Por qué funciona
One number line can only describe positions along a line. A flat grid needs two directions, so a point needs two numbers. Everyone agrees to give the across number first and the up number second, so an ordered pair means the same point to everyone.
Worked examples
Ejemplo resuelto: Plot a point
Plot $(4, 3)$.
- Start at the origin $(0, 0)$.
- The first number is 4: go 4 units right along the x-axis.
- The second number is 3: go 3 units up. Mark the point.
Respuesta: the point 4 across and 3 up
Ejemplo resuelto: Read a point
A point is 6 units right of the origin and 1 unit up. What are its coordinates?
- Across comes first: 6.
- Up comes second: 1.
Respuesta: $(6, 1)$
Error común
Swapping the coordinates and plotting $(2, 5)$ at $(5, 2)$. Remember “across, then up,” like walking along a hallway before taking the stairs. Check: the first number should match the x-axis below the point.