Transformations Project

By: Daylan Glenn

Translation

Moving a shape, without rotating or flipping it. "Sliding".
The shape still looks exactly the same, just in a different place.


For my translation I moved my original figure 3 units to the right and 1 unit down to create the new figure. since I moved right it will increase my x value and moving down will decrease my y value. it would be represented as (x+3, y-1).


taking my original ordered pairs I can see that the new ordered pairs by changing the x and y values.


D(3,2) Translated: (3+3, 2-1) D'(6,1)

A(3,6) Translated: (3+3, 6-1) A'(6,5)

Y(7,2) Translated: (7+3, 2-1) Y'(10,1)


Translation of graph below:

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Rotation

There is a central point that stays fixed and everything else moves around that point in a circle.


For my rotation I rotated my figure 270 degrees counter-clockwise around the origin (0,0) This made my ordered pairs change to (x,y) to (y,-x). This means that my original y value is now my x value. now the original x value is now an additive inverse and has became the y value.


The change that occurred to my original ordered pairs:


D(3,2) D'(2,-3)

A(3,6) A'(6,-3)

Y(7,2) Y'(2,-7)

Rotation graph below:

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Reflection

An image or shape as it would be seen in a mirror.


for my reflection I reflected my figure across the x-axis. By reflecting across the x-axis it will cause the y-value to change while the x-value remains the same. it can be represented as (x,-y).


D(3,2) Reflected: D'(3,-2)

A(3,6) Reflected: A'(3,-6)

Y(7,2) Reflected: Y'(7,-2)


Reflection graph below:

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Dilation

To re-size something in general English it means to make larger. But in math it means to make larger or smaller.


For my dilation I choose the origin of the graph (0,0) as the center of dilation and the scale factor of 2. Since my scale factor is between 1 and 2 it will create an enlargement of my original figure. By using the origin as my center of dilation I can easily do the scale factor for the original ordered pairs of my original figure. It can be showed as (2x, 2y).



D(3,2) Dilated: (2*3, 2*2) D'(6,4)

A(3,6) Dilated: (2*3, 2*6) A'(6,12)

Y(7,2) Dilated: (2*7, 2*2) Y'(14,4)


Dilation graph below. As you can see there is an enlargement on the new figure.

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