# A line segment has endpoints at #(4 ,2 )# and #(5 ,3 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated horizontally by # 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

##### 1 Answer

Jul 28, 2018

#### Explanation:

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

#"the endpoints"#

#A=(4,2)" and "B=(5,3)#

#color(blue)"first transformation"#

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

#"a point "(x,y)to(y,-x)#

#A(4,2)toA'(2,-4)#

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

#color(blue)"second transformation"#

#"under a horizontal transformation "((2),(0))#

#• " a point "(x,y)to(x+2,y)#

#A'(2,-4)toA''(4,-4)#

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

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#A''(4,-4)toA'''(4,4)#

#B''(5,-5)toB'''(5,5)#

#"After all 3 transformations"#

#(4,2)to(4,4)" and "(5,3)to(5,5)#