A line segment has endpoints at #(7 ,5 )# and #(6 ,5)#. If the line segment is rotated about the origin by #(3pi )/2 #, translated vertically by #3 #, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

#(5,4)" and "(5,3)#

#"Since there are 3 transformations to be performed label"# #"the endpoints"#
#A=(7,5)" and "B=(6,5)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#A(7,5)toA'(5,-7)#
#B(6,5)toB'(5,-6)#
#color(blue)"second transformation"#
#"under a vertical translation "((0),(3))#
#• " a point "(x,y)to(x,y+3)#
#A'(5,-7)toA''(5,-4)#
#B'(5,-6)toB''(5,-3)#
#color(blue)"third transformation"#
#"under a reflection in the x-axis"#
#• " a point "(x,y)to(x,-y)#
#A''(5,-4)toA'''(5,4)#
#B''(5,-3)toB'''(5,3)#
#"After all 3 transformations"#
#(7,5)to(5,4)" and "(6,5)to(5,3)#
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Answer 2

The new endpoints of the line segment after rotation by ( \frac{3\pi}{2} ), vertical translation by 3 units, and reflection about the x-axis are:

Endpoint 1: ((-5, 10))

Endpoint 2: ((-5, 9))

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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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