Transformations

By Sean Knox

Reflection

Reflection

For my reflection I decided to reflect my figure across the x -axis. By reflecting across the x-axis I will cause the y-value to become its additive inverse while the x-value will remain the same. It can be represented by (x, -y)

The following represents the change to my original ordered pairs to create my reflection.

A(5, 2) Reflection: (8, -2)

B(3, 6) Reflection: (3, -6)

C(8, 5) Reflection: (8, -5)


This reflection did not change the size or shape of my original triangle, therefore the new figure is congruent to the original figure. You can see the graph of my reflection in the upper left corner

Rotation

A rotation is where a figure is turned around a point of rotation that does not move. For my rotation I rotated 270 degrees counterclockwise around the origin (0, 0). This caused my ordered pairs to change from (x, y) to (y, -x). This means that my original y value is now my x value and the original x value is now its additive inverse and has become the new y-value.

This is the change that occurred to my original ordered pairs.



A(6, 9) A'(9, -6)

B(3, 5) B'(5, -3)

C(1, 7) C'(7, -2)

As you look at the ordered pairs you can see where the values changed positions.


The picture of the graph is in the top right corner

Translaton

A translation is where a figure is moved but the size and shape are not changed. Sometimes we refer to a translation as a slide.

For my translation I choose to move my original triangle five units to the left and two units up to create a new figure. Since I moved left it will decrease my x value and moving up will increase my y value. It can be represented as (x - 5, y + 2).

Taking my original ordered pairs I can determine the location of the new ordered pairs by changing the x and y values.

A(8, 9) Translation: (3 - 5, 9 + 2) A'(3, 11)

B(2, 3) Translation: (2 - 5, 3 + 2) B'(-3, 5)

C(8, 5) Translation: (8 - 5, 5 + 2) C'(3, 7)

You can see my translation in the top left corner.