Transformations
Lessons in this chapter
About Transformations
Transformations introduces the four basic ways to move or resize a figure on the coordinate plane, then connects them to congruence and similarity.
Translations, Reflections, and Rotations each move a figure without changing its size or shape, sliding it, flipping it over a line, or turning it around a point, and Congruence and Transformations ties all three together: two figures are congruent exactly when one can be mapped onto the other using only these size-preserving moves.
Dilations introduces the one transformation that does change size, scaling a figure larger or smaller from a center point, and Similarity and Transformations shows that two figures are similar exactly when one maps onto the other using dilations combined with the earlier size-preserving moves.
Perimeter and Area of Similar Figures closes the chapter with the practical payoff: once two figures are similar, their perimeters scale by the same factor as their sides, while their areas scale by that factor squared, a relationship that only makes sense once similarity itself is understood.
The seven lessons here are 8th grade math worksheets rather than reading: Translations, Rotations and Perimeter and Area of Similar Figures each give your child figures to move, map and measure directly in the page. Answers are checked question by question, which is where a rotation done in the wrong direction or a dilation scaled from the wrong center shows up. All seven are free to try, with no login needed for your first 3.
Frequently asked questions
The chapter takes one transformation at a time: Translations slides a figure, Reflections flips it across a line, and Rotations turns it about a point. Congruence and Transformations then establishes that those three leave size and shape unchanged, before Dilations introduces scaling by a factor and Similarity and Transformations defines similar figures as the result. Perimeter and Area of Similar Figures closes with how scaling a figure by k changes its perimeter by k and its area by k squared. This sits in the Common Core domain Geometry (8.G).
A transformation is a rule that moves or resizes every point of a figure: translations slide it, reflections flip it, rotations turn it, and dilations resize it, all producing a new figure called the image.
A translation slides a figure the same distance in the same direction, a reflection flips it over a line like a mirror, and a rotation turns it around a fixed point by a given angle: all three keep the figure's size and shape exactly the same.
Two figures are congruent exactly when one can be mapped onto the other using only translations, reflections, and rotations: Congruence and Transformations has kids describe the specific sequence of moves that proves two given figures are congruent.
A dilation resizes a figure larger or smaller from a fixed center point, using a scale factor: unlike translations, reflections, and rotations, a dilation changes the figure's size, though not its shape.
Two figures are similar exactly when one maps onto the other using a dilation combined with any of the size-preserving transformations: same shape, not necessarily the same size, which Similarity and Transformations has kids verify and describe.