November 10, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Translation, Reflection, Dilation, and Rotation.

In this section, you’ll learn the definition and concepts for some specific types of transformations called translation, reflection, dilation and rotation and understand their properties. While discovering, you will be explained by the instructor with the help of video and in own handwriting as well as presented some examples with solution.

A translation simply means a transformation in which a geometric figure is moved to another location without any change in size or orientation. Every point of the shape must move- the same distance and in the same direction. E.g. every translated figure is the image of the original figure. For example: in a translation, when ?ABC is moved to ?*A’B’C’*, *AA’* = *BB’* = *CC’* and *AA’* || *BB’* || *CC’*. If movement with respect to the x-axis is l units and y-axis is m units, then under a translation coordinates of point A(*x*, *y*) becomes A’(*x* + *l*, *y* + *m*).

Reflection is a transformation in which each point of a figure has an image that is the same distance from the line of reflection as the original figure i.e. every point is at the same distance from the central line and is of the same size as the original image. It may be noted that the reflection is across a line and that line is called the line of reflection. For reflection in the*x*-axis, *x* coordinates are the same and the *y* coordinates are opposite, while for reflection in *y*-axis the *y* coordinates are the same and the *x* coordinates are opposite. E.g. when point (5, 5) is translated, 4 units left and 5 units down, then new point is (1, 0). The image of point A (2, 3) after a reflection in the x-axis is A’ (2, -3).

Dilation is a geometric transformation that changes a figure's size i.e. enlarged or reduced, but its shape, orientation, and location remain the same. The point, with respect to which it takes place, is called the center of dilation. In dilation of a geometric figure, all dimensions are lengthened or shortened by a specified amount called ‘scale factor’. For example: in case of dilation of triangle*ABC* to *A’B’C’*, in which if *AB* = 2, *AC* = 4, *BC* = 5 and *A’B’* = 3, *A’C’* = 6, *B’C’* = 7.5., the scale factor is 1.5.

A rotation is a transformation in which every point of a figure moves along a circular path around a fixed point that is called the center of rotation i.e. the distance from the center to any point on the shape stays the same. For example: the number of degrees separating the blades on a four blades fan, will be 90°. It is generally specified in degree measure and with a specified direction. For example, when point (-2, 8) will rotate 90° clockwise about the origin, then its image is (8, 2).

In this section, you’ll learn the definition and concepts for some specific types of transformations called translation, reflection, dilation and rotation and understand their properties. While discovering, you will be explained by the instructor with the help of video and in own handwriting as well as presented some examples with solution.

A translation simply means a transformation in which a geometric figure is moved to another location without any change in size or orientation. Every point of the shape must move- the same distance and in the same direction. E.g. every translated figure is the image of the original figure. For example: in a translation, when ?ABC is moved to ?

Reflection is a transformation in which each point of a figure has an image that is the same distance from the line of reflection as the original figure i.e. every point is at the same distance from the central line and is of the same size as the original image. It may be noted that the reflection is across a line and that line is called the line of reflection. For reflection in the

Dilation is a geometric transformation that changes a figure's size i.e. enlarged or reduced, but its shape, orientation, and location remain the same. The point, with respect to which it takes place, is called the center of dilation. In dilation of a geometric figure, all dimensions are lengthened or shortened by a specified amount called ‘scale factor’. For example: in case of dilation of triangle

A rotation is a transformation in which every point of a figure moves along a circular path around a fixed point that is called the center of rotation i.e. the distance from the center to any point on the shape stays the same. For example: the number of degrees separating the blades on a four blades fan, will be 90°. It is generally specified in degree measure and with a specified direction. For example, when point (-2, 8) will rotate 90° clockwise about the origin, then its image is (8, 2).

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

- Mathematics > General
- Mathematics > Geometry
- Education > General

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Verify experimentally the properties of rotations, reflections, and translations:

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.