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.

• Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

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    What is an Ordered Pair?

    Ordered pairs are a fundamental part of graphing. Ordered pairs make up functions on a graph, and very often, you need to plot ordered pairs in order to see what the graph of a function looks like. This tutorial will introduce you to ordered pairs!

• Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

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    What are Similar Figures?

    Looking at two figures that are the same shape and have the same angle measurements? You have similar figures! Learn all about it in this tutorial!

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

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    What is a Transformation?

    Transformations can be really fun! They allow you to change or move a figure. In this tutorial, learn about all the different kinds of transformations!

• Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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    What is a Reflection?

    When you look in the mirror, you see your reflection. In math, you can create mirror images of figures by reflecting them over a given line. This tutorial introduces you to reflections and shows you some examples of reflections. Take a look!

• Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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    How Do You Use Coordinates to Reflect a Figure Over the Y-Axis?

    Want to see how to reflect a figure over the y-axis? Then this tutorial was made for you! In this tutorial, you'll see how to use coordinates from the original figure to reflect the figure over the y-axis. Take a look!