Recap of Rigid Transformations

​A transformation takes a figure and changes it by moving it in the coordinate plane. There are four types of transformations: reflections, rotations, translations, and dilations.

​

Three of the transformations are called "rigid transformations".  This means that the figure will be congruent to the original.  Unlike rigid transformations, dilations affect the size of the figure and create images that are similar.

​pre-image: the original

​image: the result after a transformation

• ​we can identify the image because it will be labeled with the prime symbol ( ' )

​Definition-

• ​translation: you slide a figure from one position to another without turning it.

​

​Characteristics:

• ​Creates a CONGRUENT image (same size)

• ​Does NOT change orientation (direction it faces)

​translations are often written in arrow notation

​

​for x value (horizontal movement):

• if we ADD to x, we move RIGHT

• ​if we SUBTRACT from x, we move LEFT

​

​for y value (vertical movement)

• ​if we ADD to y, we move UP

• ​if we SUBTRACT from y, we move DOWN

Definition: flips an object over a line to create a mirror image

​

​Characteristics:

• ​Creates an image that is CONGRUENT (same size)

• ​Changes orientation (direction) of pre-image

​We will focus on reflecting over 3 lines:

​x-axis

​y-axis

​y=x

​When reflecting over:

​x-axis: you keep the x value and change the sign of the y value

​y-axis: you keep the y value and change the sign of the x value

​y=x: you switch the places of the x and y value but keep their signs the same

​Definition: turns an object around a point

​

​Characteristics:

• ​Creates CONGRUENT image (same size)

• ​Changes orientation (direction)

​For rotations we need to know which direction and how many degrees we are going.

​* If you are going you flip the order of the numbers and give them the sign of the quadrant they are in.

​*If you are going either direction, you are going to

keep the order but change the signs of

both x and y values.​