Coordinate Geometry - Plotting a Point in the Plane

The Cartesian Plane is defined by two perpendicular number lines: the horizontal line called the $x$-axis and the vertical line called the $y$-axis. These lines intersect at a central point called the origin, denoted by $O(0, 0)$.

The axes divide the plane into four distinct regions called Quadrants. Moving counter-clockwise from the top-right, they are: Quadrant I $(+, +)$, Quadrant II $(-, +)$, Quadrant III $(-, -)$, and Quadrant IV $(+, -)$. Visually, this looks like a cross dividing the space into four equal zones.

Every point in the plane is identified by an ordered pair $(x, y)$. The first value $x$ is the Abscissa (perpendicular distance from the $y$-axis), and the second value $y$ is the Ordinate (perpendicular distance from the $x$-axis).

To plot a point like $P(x, y)$, you start at the origin $(0, 0)$. Move $|x|$ units along the $x$-axis (right if $x > 0$, left if $x < 0$). Then, from that position, move $|y|$ units vertically (up if $y > 0$, down if $y < 0$).

Any point situated exactly on the $x$-axis will have an ordinate of $0$, resulting in the coordinate form $(x, 0)$. For example, $(4, 0)$ lies on the positive $x$-axis.

Any point situated exactly on the $y$-axis will have an abscissa of $0$, resulting in the coordinate form $(0, y)$. For example, $(0, -5)$ lies on the negative $y$-axis.

The distance of a point $(x, y)$ from the $x$-axis is equal to $|y|$ units, and its distance from the $y$-axis is equal to $|x|$ units.