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Question 1114963: Hello! I was having difficulty answering two out of three questions I was given:
Triangle ABC has the following points:
A(4,4)
B(6,6)
C(5,2)
Given the information above, describe the new coordinates of points A, B, and C after the following transformations:
1. Translation of point A around the origin
2. 90 degree rotation around point B
3. Reflection of the triangle across the x-axis
Side note: For #3, I am pretty sure I just put a negative sign in front of the Y values because the reflection would be across the X axis!
I wanted to thank you in advance for helping me solve this problem I have been stuck on!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
1. Saying "Translation around the origin" makes no sense to be honest. A geometric translation is a vertical and/or horizontal shift of a point. So it needs to specify how much the point moves up/down as well as how much it moves left/right. It seems like a typo because rotations are often done around the origin. However, no angles are mentioned here. So again something seems odd about this.
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2. Is this rotation clockwise or counter-clockwise? It doesn't specify.
Regardless of how you rotate, one handy way to do this is to first translate point B(6,6) to the origin (0,0). So you'll subtract 6 from the x coordinate and subtract 6 from the y coordinate. Do this to every point A, B and C. The points A(4,4), B(6,6) and C(5,2) will turn into A(-2,-2), B(0,0) and C(-1,-4).
Then you'll use the rule (x,y) --> (y,-x) to rotate 90 degrees clockwise OR you'll use the rule (x,y) --> (-y,x) to rotate counter-clockwise. After the rotation is complete, you must undo the translation done earlier. So you'll add 6 to each x coordinate and add 6 to each y coordinate.
Note: Point B starts at (6,6) and it will end up at (6,6). This point is known as a fixed point (every other point will change). The reason why is because the rotation is occurring around point B.
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3. Yes you are correct. The y coordinate will change from positive to negative while the x coordinate stays the same. So for example, A(4,4) turns into (4,-4)
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Extra Info: Translations, rotations and reflections are known as rigid transformations. They preserve the distances and lengths and area of the figure. In other words, the size and shape of the triangle does not change after any of these transformations.
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