# A line segment has endpoints at #(3 , 4)# and #(1 ,9)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-2#, and reflected about the x-axis, what will the line segment's new endpoints be?

##### 1 Answer

Apr 18, 2018

#### Answer:

#### Explanation:

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

#"the endpoints"#

#A(3,4)" and "B(1,9)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(y,-x)#

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

#rArrB(1,9)toB'(9,-1)#

#color(blue)"Second transformation"#

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

#• " a point "(x,y)to(x-2,y)#

#rArrA'(4,-3)toA''(2,-3)#

#rArrB'(9,-1)toB''(7,-1)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#rArrA''(2,-3)toA'''(2,3)#

#rArrB''(7,-1)toB'''(7,1)#

#"After all 3 transformations"#

#(3,4)to(2,3)" and "(1,9)to(7,1)#