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## Grade 8 math (FL B.E.S.T.)

### Course: Grade 8 math (FL B.E.S.T.)>Unit 8

Lesson 1: Transformations intro

# Rigid transformations intro

Transformations in math involve changing a shape's position or which way the shape points. There are three main types: translations (moving the shape), rotations (turning the shape), and reflections (flipping the shape like a mirror image). Rigid transformations keep the shape's size and angles the same. The image is the shape in its new position and direction.

## Want to join the conversation?

• Is a translation and a transformation the same thing?
• No.A transformation includes rotations, reflection, and translations. Translations just slide the figure around the grid.
• what other types of transformations are there besides rigid transformations?
• Nice question!

A common type of non-rigid transformation is a dilation. A dilation is a similarity transformation that changes the size but not the shape of a figure. Dilations are not rigid transformations because, while they preserve angles, they do not preserve lengths.

Have a blessed, wonderful day!
• At 0.48 seconds, Sal said that there are an infinite number of points along the shape. I am just checking my understanding; I get that there a LOT of points but surely the number is finite as it is along a fixed 2D shape with lines connecting or have I not understood it?
• A side of a polygon is a type of line segment. Any line segment has infinitely many points, though its length is finite. Note that for any two distinct points P and Q on a line segment, no matter how close they are together, there are points (besides P and Q) on that line segment that are between P and Q.
• Is Dilation a Rigid Transformation?
• Dilations are not a rigid transformations. For something to be a rigid transformation, angles and side lengths need to stay the same. Dilations increase the size of sides.
• What are the different types of translations?
• A translation (or "slide") is one type of transformation.

In a translation, each point in a figure moves the same distance in the same direction.

Example:
If each point in a square moves 5 units to the right and 8 units down, then that is a translation!

Another example:
If each point in a triangle moves 3 units to the left, and there is no up or down movement, then that is also a translation!

Hope this helps!
• Can someone explain rotations. I think I got Translations and Reflections, but not rotations I have always been stuck on it. Thank you!
• There are 3 main types of rotations:
1.) 90∘ clockwise - To move a point or shape 90∘ clockwise, simply use this equation: (x, y) → (y, −x).
2.) 90∘ counterclockwise - To move a point or shape 90∘ counterclockwise, simply use this equation: (x, y) → (−y, x).
3.) 180∘ rotation - To move a point or shape 180∘, simply use this equation: (x, y) → (−x, −y).
If a question asks for a 270∘ clockwise rotation, simply change it to a 90∘ counterclockwise, and vice versa. I hope this helped! Thank you for asking! :)
• will this be taught in geometry?
• In most geometry courses this is taught early into the semester.
• How do you know how many degrees to turn the shape for rotation?

deeply greatfull
• I have that problem, too. But you only need to figure out how many degrees does the shape looking have. It needs more experience to do it.
• what kind of transformation is a dilation?