Why is dilation not an isometry?
Caroline AucoinBecause dilation "amplify" or "reduce" distance between image points. An isometry conserve distance between points
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Aurora AyalaDilation is not an isometry because it changes the size of an object while preserving its shape and orientation. Isometries, also known as rigid transformations, include translations, rotations, and reflections, which preserve distances and angles between points. Dilation, on the other hand, alters distances between points by stretching or shrinking them uniformly in all directions from a fixed center point. Therefore, dilation does not preserve distances and angles, making it distinct from isometries.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- Image point B'(4,-8) was transformed using the translation (x-2, y+ 3). What were the coordinates of B?
- A line segment with endpoints at #(1 , -2 )# and #(5, 9 )# is rotated clockwise by #(3 pi)/2#. What are the new endpoints of the line segment?
- A line segment has endpoints at #(1 ,4 )# and #(4 , 9)#. The line segment is dilated by a factor of #1/3 # around #(4 , 2)#. What are the new endpoints and length of the line segment?
- A line segment has endpoints at #(8 ,4 )# and #(3 ,7 )#. The line segment is dilated by a factor of #1/2 # around #(3 ,2 )#. What are the new endpoints and length of the line segment?
- A dilation with center (0, 0) and scale factor k is applied to a polygon. What dilation can you apply to the image to return it to the original preimage?
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