Similarity and Transformations

By: Philip Brown

All About Tranformations

Transformations have four main parts or types of transformation. They are Translation, Reflection, Rotation, and Dilation. I will be covering each of these.


Translation

A Translation is transformation that slides a figure from one position to the other with turning.

Vocabulary:

Pre-image

X-Coordinate

Y-Coordinate

Congruent

When a figure is translated the x-axis is changing the y axis and y -axis changes the x-axis.

(x,y)-->(x+a, y+b)

Reflection

A Reflection is a mirror image of the original figure.

Vocabulary:

reflection

line of reflection

When you reflect a figure over the x-axis you multiply the y-coordinate by -1.

When you reflect a figure over the y-axis you multiply the x-coordinate by -1.

Rotation!

A Rotation is a transformation in which a figure is rotated, or turned, about a fixed point.

Vocabulary:

Rotation

Center of Rotation

x-coordinate

y-coordinate

Each point of the original figure and its image is the same distance from the center of rotation.

Dilation!

A dilation is a transformation that enlarges or reduces a figure by a scale factor.

Vocabulary

X axis

Y axis

Scale

Factor

When the center of dilation in the coordinate plane is the origin, each coordinate of the preimage  is multiplied by the scale factor k to find the coordinates of the image.

(x,y)--->(kx,ky)

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