Background Tutorials

• Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

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    What is the Coordinate Plane?

    You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.

• Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

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    How Do You Plot Points in the Coordinate Plane?

    Knowing how to plot ordered pairs is an essential part of graphing functions. In this tutorial, you'll see how to take an ordered pair and plot it on the coordinate plane. Take a look!

• Lines are taken to lines, and line segments to line segments of the same length.

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    What is a Translation?

    Ever slide something across a table? If so, then you have performed a translation! In this tutorial, learn the definition of translation and see some really neat examples. Take a look!

• Add, subtract, and multiply matrices of appropriate dimensions.

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    How Do You Add Matrices?

    Adding matrices is easier than you might think! Just find the corresponding positions in each matrix and add the elements in them! This tutorial can show you the entire process step-by-step.

• Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

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    What is an Image?

    Just about everything in math has a name! Did you know that when you're dealing with transformations, the new figure you get is called an image? Check out this tutorial and learn about this math term!