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.
- A line segment has endpoints at #(2 , 2)# and #(5 , 4)#. If the line segment is rotated about the origin by #(pi)/2 #, translated horizontally by #1#, and reflected about the y-axis, what will the line segment's new endpoints be?
- Circle A has a radius of #3 # and a center of #(2 ,1 )#. Circle B has a radius of #2 # and a center of #(7 ,8 )#. If circle B is translated by #<4 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Points A and B are at #(3 ,7 )# and #(2 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #4 #. If point A is now at point B, what are the coordinates of point C?
- Point A is at #(4 ,-5 )# and point B is at #(-6 ,-2 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- A triangle has corners at #(2 ,-2 )#, #(3 ,-1 )#, and #(5 ,7 )#. If the triangle is dilated by a factor of #2/5 # about point #(6 ,-2 ), how far will its centroid move?
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