In Grade 5 you plotted points to the right of and above the origin (see Points on the Coordinate Plane). Now each axis is a full number line, with negative numbers too, so the plane has four parts.
Idea clave
A point $(x, y)$: start at the origin, move $x$ left or right, then $y$ down or up. The four quadrants are numbered counterclockwise from the top right: I $(+, +)$, II $(-, +)$, III $(-, -)$, IV $(+, -)$.
Por qué funciona
The x-axis is a number line, so negative x means left. The y-axis is a number line standing up, so negative y means down. Reflecting a point across an axis puts it the same distance from that axis on the other side, so one coordinate changes to its opposite: across the x-axis $(x, y) \to (x, -y)$, across the y-axis $(x, y) \to (-x, y)$.
Ejemplo resuelto: Plot and name the quadrant
Plot $(-3, 2)$. Which quadrant is it in?
- Start at the origin. $x = -3$: move 3 left.
- $y = 2$: move 2 up.
- Left and up is Quadrant II.
Respuesta: Quadrant II
Ejemplo resuelto: Reflect
Reflect $(4, -1)$ across the y-axis.
- Across the y-axis the point moves left or right, so x changes sign.
- $4$ becomes $-4$; $y$ stays $-1$.
Respuesta: $(-4, -1)$
Ejemplo resuelto: On an axis
Where is $(0, 4)$?
- $x = 0$: no move left or right.
- $y = 4$: 4 up. The point is on the vertical axis.
Respuesta: On the y-axis (not in any quadrant).
Error común
Two mix-ups are common. One is swapping the coordinates and plotting $(-3, 2)$ at $(2, -3)$: x always comes first, like "walk before you climb". The other is putting $(0, 4)$ on the x-axis. Quick check: a 0 in the x spot means you never moved sideways, so you are still on the y-axis.