Points A and B are at #(7 ,1 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?

Answer 1

#C=(15,3)#

#"under a counterclockwise rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#rArrA(7,1)toA'(-1,7)" where A' is the image of A"#
#rArrvec(CB)=color(red)(1/2)vec(CA')#
#rArrulb-ulc=1/2(ula'-ulc)#
#rArrulb-ulc=1/2ula'-1/2ulc#
#rArr1/2ulc=ulb-1/2ula'#
#color(white)(rArr1/2ulc)=((7),(5))-1/2((-1),(7))=((15/2),(3/2))#
#rArrulc=2((15/2),(3/2))=((15),(3))#
#rArrC=(15,3)#
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Answer 2

The coordinates of point C after the described transformations are (7, 3).

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Answer from HIX Tutor

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.

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