# A triangle has corners at #(3, -5 )#, ( 2 , -1)#, and #( 4 , 3)#. What will the new coordinates of the triangle be if it is reflected across the x-axis?

Under a reflection in the x-axis a point

Under a reflection in the y-axis a point

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The new coordinates of the triangle after reflecting it across the x-axis are:

(3, 5), (2, 1), and (4, -3).

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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.

- Points A and B are at #(9 ,7 )# and #(2 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?
- Circle A has a radius of #2 # and a center of #(6 ,5 )#. Circle B has a radius of #3 # and a center of #(2 ,4 )#. If circle B is translated by #<1 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Point A is at #(4 ,2 )# and point B is at #(3 ,6 )#. Point A is rotated #pi/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 ,3 )#, #(1 ,-2 )#, and #(-6 ,6 )#. If the triangle is dilated by a factor of #5 # about point #(-3 ,2 ), how far will its centroid move?
- A line segment has endpoints at #(7 ,4 )# and #(5 ,9)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #5 #, and reflected about the y-axis, what will the line segment's new endpoints be?

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