Quiz: Linear Inequalities and Half-PlanesĬoordinate geometry deals with graphing (or plotting) and analyzing points, lines, and areas on the coordinate plane (coordinate graph).Solving Equations Containing Absolute Value.Inequalities Graphing and Absolute Value.Quiz: Operations with Algebraic Fractions.Quiz: Solving Systems of Equations (Simultaneous Equations).Solving Systems of Equations (Simultaneous Equations).Quiz: Variables and Algebraic Expressions.Quiz: Simplifying Fractions and Complex Fractions.Simplifying Fractions and Complex Fractions.Quiz: Signed Numbers (Positive Numbers and Negative Numbers).Signed Numbers (Positive Numbers and Negative Numbers).Quiz: Multiplying and Dividing Using Zero.Quiz: Properties of Basic Mathematical Operations.Properties of Basic Mathematical Operations. For example, we can represent the point \left(3,-1\right) in the plane by moving three units to the right of the origin in the horizontal direction and one unit down in the vertical direction. An ordered pair is also known as a coordinate pair because it consists of x and y-coordinates. Together we write them as an ordered pair indicating the combined distance from the origin in the form \left(x,y\right). The axes extend to positive and negative infinity as shown by the arrowheads in the figure below.Įach point in the plane is identified by its x-coordinate, or horizontal displacement from the origin, and its y-coordinate, or vertical displacement from the origin. From the origin, each axis is further divided into equal units: increasing, positive numbers to the right on the x-axis and up the y-axis decreasing, negative numbers to the left on the x-axis and down the y-axis. It is known as the origin or point \left(0,0\right). The center of the plane is the point at which the two axes cross. Each section is called a quadrant the quadrants are numbered counterclockwise as shown in the figure below. Perpendicular to each other, the axes divide the plane into four sections. The Cartesian coordinate system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the x-axis and the y-axis. Descartes named the horizontal axis the x-axis and the vertical axis the y-axis. While there is evidence that ideas similar to Descartes’ grid system existed centuries earlier, it was Descartes who introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Further, by dividing each axis into equal unit lengths, Descartes saw that it was possible to locate any object in a two-dimensional plane using just two numbers-the displacement from the horizontal axis and the displacement from the vertical axis. He viewed the perpendicular lines as horizontal and vertical axes. According to the story, Descartes was staring at a fly crawling on the ceiling when he realized that he could describe the fly’s location in relation to the perpendicular lines formed by the adjacent walls of his room. Plot points on the Cartesian coordinate plane.Īn old story describes how seventeenth-century philosopher/mathematician René Descartes invented the system that has become the foundation of algebra while sick in bed.Define the components of the Cartesian coordinate system.
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