A line segment has endpoints at #(5 ,9 )# and #(8 ,7 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

#A''' = [(-1, 0), (0, 1)] [(-9 ), (-3)]=[(9), (-3)]#

#B''' = [(-1, 0), (0, 1)] [(-7), (0)]=[(7), (0)]#

Given : Two points #A(5,9)# and #B(8,7)#. Rotate by #pi/2#, translate vertically -8 and reflected about y-axis Required : New end-point of the segment #A'# and #B'# Solution Strategy : a) Rotate b) Translated Vertically c) Reflect
a) Rotate using Rotation Matrix : #R(pi/2) = [(cos(pi/2), -sin(pi/2)), (sin(pi/2), cos(pi/2))]=[(0, -1), (1, 0)]# #A' = [(0, -1), (1, 0)] [(5 ), (9)]=[(-9), (5)]#
#B' = [(0, -1), (1, 0)] [(8), (7)]=[(-7), (8)]#
b) Translate Vertically : Translation Operation of vector, #P# by #delta_(x,y)# is given by: #vec(P') = vecP + vecdelta_(x,y) # where #delta_(x,y)=[(delta_x), (delta_y)]# thusd #A'' = [(-9), (5)] + [(0), (-8)]=[(-9), (-3)]#
#B''=[(-7), (8)]+[(0), (-8)]= [(-7), (0)]=#
c) Reflection Vertically : Reflection Matrix about y, is #Rf_y=[(-1, 0), (0, 1)]# #A''' = [(-1, 0), (0, 1)] [(-9 ), (-3)]=[(9), (-3)]#
#B''' = [(-1, 0), (0, 1)] [(-7), (0)]=[(7), (0)]#
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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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