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### Course: Basic geometry and measurement>Unit 14

Lesson 5: Properties & definitions of transformations

# Mapping shapes

Let's find the right sequence of rigid transformations (like rotations, translations, and reflections) to map one triangle onto another. Different sequences can work, but order matters. So, it's important to test each one to see if it maps the triangles correctly.

## Want to join the conversation?

• When I do the "Mapping Shapes" exercise, often times I have it matching up exactly with the shape, except for the fact that it seems that the shape is slightly smaller than the one one the graph originally. It doesn't matter what the shape is, it always happened, and it's leaving me really frustrated and angry at myself. Can anyone help me with this issue please?
• This may be because two of your sides almost look alike, but are not, as in a quadrilateral with two sides differing by one unit.
hope this helps with people who are reading this and about to do the practice.
• What does "a translation along the directed line segment HD" mean..Sal didn't teach about this kind of problem on mapping shapes.
• Nicholas Hood-Daniel gave the answer in the comments though so full credits to him:

it means putting point h to point d from one shape to the other and just draw the rest of the points in the same configuration as the pre image
• With the second example, why couldn't Sal just reflect the shape, instead of transforming and then reflecting?
• because the reflection is relative to a point. transforming it and then reflecting vs. reflecting and then transforming will get you a different answer. its easier to show this with visuals so I recommend trying out the question yourself to see the difference.
(1 vote)
• You could change the playback speed if it is too fast
If it does not work then maybe get an extension that will change the speediness of this video
• I really can't grasp the concept of this, can someon reply with the basics? I will be very much thankful
• This might be a little late, and I am not sure if this will help, but I will try.(Also, if they are any grammatical mistakes, please forgive that.)
So, first to understand this, you must know and understand the concept of 4 transformations: Translations, Rotations, Dilations, and Reflections. Translation is basically moving an image by a certain number of x and y coordinates, without changing anything. Rotations are when you rotate a shape by some amount of degree, usually 90, 180, or 270 degrees. Dilations are when you shrink or enlarge a shape. Finally, a reflection is basically when you reflect an image or a coordinate point across a line. This line could be x-axis, y-axis, or any other line the problem specifies.
In this video, Sal, the one who is talking in the video, is trying to find which sequences could transform the image PQR to ABC. To do that, multiple transformations were applied. Trying to find which transformations were applied is what all this video and the concept is trying to explain and find. Also, note that there is more than one way to apply the transformation from PQR to ABC.

I hope this helped :)
• What is a translation over a directed line segment?
• A directed line segment is a segment that has not only a length (the distance between its endpoints), but also a direction (which means that it starts at one of its endpoints and goes in the direction of the other endpoint).

For example, directed line segment 𝐴𝐵 starts at 𝐴 and ends at 𝐵 (not the other way around).

A translation over directed line segment 𝐴𝐵 means that we are translating a point from its current location at 𝑃 to its new location at 𝑄, such that directed line segment 𝑃𝑄 has the same distance and direction as 𝐴𝐵.
• I dont get any of this I'm going to sue.
• ahaha I'm trying to catch up in my studies, since I missed a day due to someone pitching a fight with me, giving me a horribly sprained wrist yesterday, and this makes absolutely no sense! I think a good way to clear it up could potentially be to just figure it out ever so slowly through logical thinking, but of course, that could take some time. There will most certainly be a clearer, more solid, and better answer than this, so ask around, maybe someone can help!
• I do not have a good imagination, so I find this exercise pretty much impossible
• Like Darran said, use graph paper to Practice practice practice. Imagination is just like any other skill, it can be trained (unless you have aphantasia). I too am not a visual learner, but with practice it comes.