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# Linear Algebra Ch. 6

### Transformations and Similarity

Term | Definition |
---|---|

congruent | When two shapes have exactly the same shape and size. These shapes are similar and have a scale factor of 1. |

conjecture | An educated guess that often results from noticing a pattern. |

corresponding parts | Points, sides, edges, or angles in two or more figures that are images of each other with respect to a transformation. If two figures are congruent, then these parts of the figures are congruent to each other. |

dilation | A transformation which produces a figure similar to the original by proportionally shrinking or stretching the figure. In this transformation, a shape is stretched (or compressed) proportionally from a point, called the point of dilation. |

enlarge | To make larger. |

linear equation | An equation in two variables whose graph is a line. The standard form is ax + by = c. Most can be written in y = mx + b form, which is more useful for determining the line's slope and y-intercept. |

point of intersection | A point that the graphs of two equations have in common. Two graphs may have one, several, or none. The ordered pair representing this(these) points gives a solution to the equations of each of the graphs. |

reduce | To make smaller |

reflection | A transformation across a line that produces a mirror image of the original (pre-image) shape.This is called the “image” of the original figure. The line is called a “line of reflection.” It is also sometimes referred to as a “flip.” |

rigid transformations | Movements of figures that preserve their shape and size. Also called “rigid transformations.” Examples of rigid motions are reflections, rotations, and translations. |

rotation | A transformation that turns all of the points in the original (pre-image) figure the same number of degrees around a fixed center point (such as the origin on a graph). |

scale factor | A ratio that compares the sizes of the parts of one figure or object to the sizes of the corresponding parts of a similar figure or object. In this course it is also referred to as the multiplier. |

similar figures | A figure that has the same shape but are not necessarily the same size. In these types of figures, the measures of corresponding angles are equal and the ratio of the corresponding sides lengths are equal. |

system of equations | A set of equations with the same variables. Solving means finding one or more solutions that make each of the equations in the system true. A solution gives a point of intersection of the graphs of the equations in the system. |

translation | A transformation that preserves the size, shape, and orientation of a figure while sliding (moving) it to a new location. Sometimes referred to as a “slide.” |

y-intercept | The point(s) where a graph intersects the y-axis. The y-intercept of a graph is important because it often represents the starting value of a quantity in a real-world situation. |

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EMarshall8