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### Course: Geometry (FL B.E.S.T.)>Unit 3

Lesson 3: Properties & definitions of transformations

# Sequences of transformations

Determining whether segment lengths and angle measures are preserved under a given sequence of transformations.

## Want to join the conversation?

• I do not understand how to do a sequence of transformation.
• translation: move the object from one place to another.(both preserved)
dilation: change sizes of the object.(only angles preserved)
rotation: rotates the object(both preserved)
reflection: just draw a straight line and reflect the object over the line. (both preserved)
stretches about any points of the object: neither preserved because segment lengths and angle measures are both changed.

a sequence of transformation is a sequence which you follow the steps and see whether which is preserved.
Easy!
• What is stretching ? something other than dilation ?
• if you apply dilation to an object, every sides become bigger or smaller to the same ratio. For example, for a triangle ABC, after applying dilation, it becomes A'B'C' and AB:A'B'=BC:B'C'=AC:A'C'
A stretching is simply just moving the points/lines around while fixing the other points in place!
So they are completely different.
• Isn't a vertical stretch a dilation, and doesn't dilation preserve angle measure?
• A dilation stretches (or shrinks) a figure in all directions, not just vertically, and maps a figure to a geometrically similar figure. However, a vertical stretch (or shrink) does not map a figure to a geometrically similar figure.

In short: while a dilation and a vertical stretch both change the size, only a dilation preserves the shape (angles).
• At , how is the moon large enough to block the sun? Isn't the sun way larger than the moon?
• The sun is way larger than the moon, but it is much farther away from Earth than the moon is. This is what allows the moon to block out the sun's light when everything is lined up perfectly. This phenomena is called a "solar eclipse" and if you Google it you can see some examples.
• dude cant you explain why it needs to be preserved because this is so fricking confusing. you literally only tell me if its preserved or not but the questions want to know what is preserved
• Preserve means to save/keep something. In this case:
translation: move the object from one place to another.(both preserved)
dilation: change sizes of the object.(only angles reserved)
rotation: rotates the object(both preserved)
reflection: just draw a straight line and reflect the object over the line. (both preserved)
stretches about any points of the object: neither preserved because segment lengths and angle measures are both changed.

a sequence of transformation is a sequence which you follow the steps and see whether which is preserved.
Easy!
• Where are vertical and horizontal stretches defined/explained? I feel like this is a new concept and is not explained previously. Dilations are covered in the previous section, but not vertical/horizontal stretches.
• i am confusing about the stretching ,
it said stretch about line PQ,
where is the line PQ?

why is is only moving only point A and B?
why not all points A, B and C move together ?
• Well, Sal is only using points A and B as an example to show that any type stretch will not preserve the angle measures and segment lengths. So wherever line PQ is, the angle measures and segment lengths will always change. And if points A, B, and C move together, then it would not be a stretch because the shape would remain the same.
• Is there a transformation that preserves segment length but changes angles?
• If you are talking about rectangles, triangles, and other similar two-dimensional shapes, I think not. If it's a triangle and all segment lengths are preserved, remember that only one triangle can be made. If it's a parallelogram, then the changing of angle will change the shape entirely. The change would not be a geometrical transformation.