Geometry - Coordinates and Grid References

The Coordinate Plane is a two-dimensional flat surface formed by the intersection of two perpendicular lines. Visually, it looks like a grid of squares where every point can be identified by its position relative to the two main lines.

The x-axis and y-axis are the two main reference lines. The x-axis is the horizontal line (running left to right) and the y-axis is the vertical line (running up and down). They meet at a right angle to form a cross-like structure.

The Origin is the specific point where the x-axis and y-axis intersect. On a visual grid, this is the starting point for all counting and is labeled with the coordinates $(0, 0)$.

Ordered Pairs are written as $(x, y)$ and are used to locate points on the grid. The first number ($x$) represents the horizontal position, and the second number ($y$) represents the vertical position. Remember the rule: 'Go along the hallway ($x$), then up the stairs ($y$)'.

Grid References are a way of naming a specific square or region on a map. Unlike coordinates which mark a specific point, grid references often use a letter for the column and a number for the row, such as $B3$ or $G7$.

Plotting a Point means drawing a dot at a specific location on the grid. To plot $(4, 2)$, you would find the number $4$ on the horizontal x-axis, then move up until you are level with the number $2$ on the vertical y-axis.

Movement on a Grid involves changing the coordinates. Moving to the right increases the $x$ value, moving to the left decreases the $x$ value, moving up increases the $y$ value, and moving down decreases the $y$ value.