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A line segment has endpoints at #(7 ,3 )# 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

Ella Armstrong

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

#"Since there are 3 transformations to be performed label"# #"the endpoints"#

#A(7,3)" and "B(6,5)#

#color(blue)"First transformation"#

#"under a rotation about the origin of "(3pi)/2#

#• " a point "(x,y)to(y,-x)#

#rArrA(7,3)toA'(3,-7)#

#rArrB(6,5)toB'(5,-6)#

#color(blue)"Second transformation"#

#"under a vertical translation "((0),(3))#

#• " a point "(x,y)to(x,y+3)#

#rArrA'(3,-7)toA''(3,-4)#

#rArrB'(5,-6)toB''(5,-3)#

#color(blue)"Third transformation"#

#"under a reflection in the x-axis"#

#• " a point "(x,y)to(x,-y)#

#rArrA''(3,-4)toA'''(3,4)#

#rArrB'')5,-3)toB'''(5,3)#

#"After all 3 transformations"#

#(7,3)to(3,4)" and "(6,5)to(5,3)#

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Answer 2

Aurora Ayala

The new endpoints of the line segment after rotation, vertical translation, and reflection about the x-axis are (-3, 4) and (-5, 3).

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