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Study Guides > College Algebra

Summary: Points and Lines in the Plane

Key Concepts

  • We can locate, or plot, points in the Cartesian coordinate system using ordered pairs, which are defined as displacement from the x-axis and displacement from the y-axis.
  • An equation can be graphed in the plane by creating a table of values and plotting points.
  • Using a graphing calculator or a computer program makes graphing equations faster and more accurate. Equations usually have to be entered in the form y=_____.
  • Finding the x- and y-intercepts can define the graph of a line. These are the points where the graph crosses the axes.
  • The distance formula is derived from the Pythagorean Theorem and is used to find the length of a line segment.
  • The midpoint formula provides a method of finding the coordinates of the midpoint dividing the sum of the x-coordinates and the sum of the y-coordinates of the endpoints by 2.

Glossary

Cartesian coordinate system a grid system designed with perpendicular axes invented by René Descartes equation in two variables a mathematical statement, typically written in x and y, in which two expressions are equal graph in two variables the graph of an equation in two variables, which is always shown in two variables in the two-dimensional plane intercepts the points at which the graph of an equation crosses the x-axis and the y-axis ordered pair a pair of numbers indicating horizontal displacement and vertical displacement from the origin; also known as a coordinate pair, (x,y)\left(x,y\right) origin the point where the two axes cross in the center of the plane, described by the ordered pair (0,0)\left(0,0\right) quadrant one quarter of the coordinate plane, created when the axes divide the plane into four sections x-axis the common name of the horizontal axis on a coordinate plane; a number line increasing from left to right x-coordinate the first coordinate of an ordered pair, representing the horizontal displacement and direction from the origin x-intercept the point where a graph intersects the x-axis; an ordered pair with a y-coordinate of zero y-axis the common name of the vertical axis on a coordinate plane; a number line increasing from bottom to top y-coordinate the second coordinate of an ordered pair, representing the vertical displacement and direction from the origin y-intercept a point where a graph intercepts the y-axis; an ordered pair with an x-coordinate of zero   distance formula a formula that can be used to find the length of a line segment if the endpoints are known midpoint formula a formula to find the point that divides a line segment into two parts of equal length

 

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