A line segment has endpoints at #(2 , 3)# and #(1 , 2)#. If the line segment is rotated about the origin by #(pi)/2 #, translated vertically by #4#, and reflected about the xaxis, what will the line segment's new endpoints be?
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To find the new endpoints of the line segment after the described transformations:

Rotation by ( \frac{\pi}{2} ) about the origin: Applying the rotation matrix for a point ( (x, y) ) by angle ( \theta ) counterclockwise: [ \begin{pmatrix} x' \ y' \end{pmatrix} = \begin{pmatrix} \cos(\theta) & \sin(\theta) \ \sin(\theta) & \cos(\theta) \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} ] Substituting ( (2, 3) ) and ( (1, 2) ) into this formula, you will get the new coordinates after rotation.

Translation vertically by 4: Adding 4 to the ycoordinates of the points obtained from the rotation.

Reflection about the xaxis: For a point ( (x, y) ), its reflection about the xaxis becomes ( (x, y) ).
Performing these transformations sequentially will give you the new endpoints of the line segment.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
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 Circle A has a radius of #2 # and a center at #(3 ,1 )#. Circle B has a radius of #4 # and a center at #(8 ,3 )#. 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?
 A triangle has corners at #(3 ,1 )#, #(5 ,6 )#, and #(4 ,7 )#. If the triangle is dilated by a factor of #1/3 # about point #(2 ,1 ), how far will its centroid move?
 A line segment has endpoints at #(3 ,2 )# and #(6 ,8 )#. The line segment is dilated by a factor of #4 # around #(1 ,3 )#. What are the new endpoints and length of the line segment?
 A triangle has corners at #(3, 2 )#, ( 2, 1)#, and #( 5, 8)#. If the triangle is reflected across the xaxis, what will its new centroid be?
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