What is a dilation, or scaling around a point?
When scaling a plane around a point, the result is a plane of a different size but the same shape.
It is highly-recommended to draw everything out. SCALING FROM A CENTERPOINT Scaling is commonly done about
and you can see that the In this scenario, it is clearer what has happened to each point. In general, scaling about a central point is given as: SCALING OFF-CENTER Scaling might also be done from an arbitrary non-central point. For instance, scaling a triangular plane
for which You can see that
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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.
- Circle A has a radius of #2 # and a center at #(5 ,6 )#. Circle B has a radius of #5 # and a center at #(2 ,4 )#. If circle B is translated by #<-2 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Point A is at #(5 ,1 )# and point B is at #(2 ,-4 )#. 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 line segment has endpoints at #(7 ,2 )# and #(3 , 2 )#. If the line segment is rotated about the origin by #(3 pi ) /2 #, translated vertically by # -4 #, and reflected about the y-axis, what will the line segment's new endpoints be?
- A triangle has corners at #(3, 5 )#, ( 6, 2)#, and #( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment has endpoints at #(5 ,3 )# and #(5 ,4)#. If the line segment is rotated about the origin by #pi /2 #, translated horizontally by #-1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

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