# A line segment has endpoints at #(4 ,7 )# and #(5 ,3 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated horizontally by # - 2 #, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 2 Answers

#color(brown)("After all 3 transformations " color(green)((4, 7)to(-5, -4)" and "(5, 3)to(-1, -5)#

#### Explanation:

#"since there are 3 transformations to be performed"#

#"label the endpoints"#

#A(4, 7)" and "B(5, 3)#

#color(indigo)"transformation of rotation about the origin of "(3pi) / 2#

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

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

#color(indigo)"next transformation under a horizontal translation " ((-2),(0))#

#• " a point "(x,y)to(x - 2, y)#

#rArrA'(7, -4) to A''(5, -4)#

#rArrB'(3, -5) to B''(1, -5)#

#color(indigo)"last transformation under a reflection in the y -axis"#

#• " a point "(x,y)to(-x, y)#

#rArrA''(5, -4)toA'''(-5, -4)#

#rArrB''(1, -5)toB'''(-1, -5)#

#color(brown)("After all 3 transformations " color(green)((4, 7)to(-5, -4)" and "(5, 3)to(-1, -5)#

#### Explanation:

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

#"the endpoints"#

#A=(4,7)" 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(4,7)toA'(7,-4)#

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

#color(blue)"second transformation"#

#"under a horizontal translation "((-2),(0))#

#• " a point "(x,y)to(x-2,y)#

#A'(7,-4)to(A''(5,-4)#

#B'(3,-5)toB''(1,-5)#

#color(blue)"third transformation"#

#"under a reflection about the y-axis"#

#• " a point "(x,y)to(-x,y)#

#A''(5,-4)toA'''(-5,-4)#

#B''(1,-5)toB'''(-1,-5)#

#"After all 3 transformations"#

#(4,7)to(-5,-4)" and "(5,3)to(-1,-5)#