Points A and B are at #(8 ,3 )# and #(5 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?

Answer 1

#C(-11,12)#

#"under a counterclockwise rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#A(8,3)toA'(-3,8)" where A' is the image of A"#
#vec(CB)=color(red)(2)vec(CA')#
#ulb-ulc=2(ula'-ulc)#
#ulb-ulc=2ula'-2ulc#
#ulc=2ula'-ulb#
#color(white)(ulc)=2((-3),(8))-((5),(4))#
#color(white)(ulc)=((-6),(16))-((5),(4))=((-11),(12))#
#rArrC=(-11,12)#
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Answer 2

The coordinates of point C are (4, 6).

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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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