# Point A is at #(-7 ,3 )# and point B is at #(5 ,4 )#. Point A is rotated #pi # 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?

The distance has decreased by

Given:

A

The coordinate rule for a

Using the coordinate rule:

The distance formula is

The distance between point

The distance between the rotated point

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After rotating point A (originally at (-7, 3)) by π radians clockwise about the origin, the new coordinates of point A will be (7, -3). The distance between the original point A and point B (at (5, 4)) can be calculated using the distance formula. After the rotation, the distance between the new point A and point B will be the same as the original distance, as rotation about the origin does not change the distance between two points.

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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 #(7 ,1 )# and #(3 ,7 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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?
- If the following graph is of a function #f(x)#, how will the graph of (i) #f(x+3)#, (ii) #f(x)+3#, (iii) #-f(x)# and (iv) #1-f(x-3)# appear?
- Point A is at #(9 ,3 )# and point B is at #(1 ,-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?
- Circle A has a radius of #4 # and a center of #(5 ,3 )#. Circle B has a radius of #3 # and a center of #(1 ,4 )#. If circle B is translated by #<2 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- A triangle has corners at #(2 ,-5 )#, #(-1 ,2 )#, and #(3 ,-3 )#. If the triangle is dilated by a factor of #2/5 # about point #(-1 ,3 ), how far will its centroid move?

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