Similarities & Transformations
What you need to know about Transformations:
There are 4 types of Transformations:
Translation is a transformation that slides a figure from one position to another without turning the figure. In order to translate a figure you must move the vertex of the figure how ever many units to the right or left and how ever many units up and down. If you have to move to the left, it is negative. If you have to move to the right, it is positive. When you move up it's positive and when you move down it's negative.
Example: A(2,4) B(4,4) C(5,2) D(2,1) translated 7 units to the left and 3 units down would be A'(-5,1) B'(-3,1) C'(-2,-1) D'(-5,-2)
A reflection is when a figure is reflected over the x or y-axis. Also known as a flip
A dilation is an enlargement, or an image larger than the original if the scale factor is greater than 1. k>1 A reduction, or an image larger than the original if the scale factor is less than 0. 0
A(-2,-2) B(1,-1) C(0,2) after a dilation with a scale factor of 2
A(-2,-2)-->(2 x-2, 2 x-2)-->(-4,-4)
B(1,-1)-->(2 x 1, 2 x -1)-->(2,-2)
C(0,2)-->(2 x 0, 2 x 2)-->(0,4)
So, the coordinates after the dilation would be A'(-4,-4) B'(2,-2) C'(0,4)
A rotation is a transformation in which a figure is rotated, or turned, about a fixed point. Each point point of the original figure and its image are the same distance from the center of rotation. There are 3 rotations about the origin: 90 degrees, 180 degrees and 270 degrees.
When rotating 90 degrees about the origin, you switch the position of the numbers and make the x-axis the opposite.
When rotating a figure 180 degrees you keep the position of the numbers but make them both the opposite of the original number.
Rotating a figure 270 degrees requires you to switch the position of the numbers and make the y-axis the opposite of the original number.
You know two figures are similar if the second can be obtained from the first by a sequence of transformations and dilations.
Similar figures have the same shape, but may have different sizes. The sizes of the two figures are related to the scale factor of the dilation.