Summary: Plotting Points on the Rectangular Coordinate System

• Plotting Points
• Identifying Quadrants
• Verifying Solution to Linear Equation

Key Concepts

• Sign Patterns of the Quadrants

  Quadrant I	Quadrant II	Quadrant III	Quadrant IV
  $(x,y)$	$(x,y)$	$(x,y)$	$(x,y)$
  $(+,+)$	$(−,+)$	$(−,−)$	$(+,−)$

• Coordinates of Zero
  • Points with a $y$-coordinate equal to $0$ are on the x-axis, and have coordinates $(a, 0)$.
  • Points with a $x$-coordinate equal to $0$ are on the y-axis, and have coordinates $(0, b)$.
  • The point $(0, 0)$ is called the origin. It is the point where the x-axis and y-axis intersect.

Glossary

linear equation

An equation of the form $Ax+By=C$, where $A$ and $B$ are not both zero, is called a linear equation in two variables.

ordered pair

An ordered pair $\left(x,y\right)$ gives the coordinates of a point in a rectangular coordinate system. The first number is the $x$ -coordinate. The second number is the $y$ -coordinate. $\underset{x\text{-coordinate},y\text{-coordinate}}{\left(x,y\right)}$

origin

The point $\left(0,0\right)$ is called the origin. It is the point where the the point where the $x$ -axis and $y$ -axis intersect.

quadrants

The $x$ -axis and $y$ -axis divide a rectangular coordinate system into four areas, called quadrants.

solution to a linear equation in two variables

An ordered pair $\left(x,y\right)$ is a solution to the linear equation $Ax+By=C$, if the equation is a true statement when the x- and y-values of the ordered pair are substituted into the equation.

x-axis

The x-axis is the horizontal axis in a rectangular coordinate system.

y-axis

The y-axis is the vertical axis on a rectangular coordinate system.

Licenses & Attributions