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

##### 1 Answer

Dec 9, 2017

#### Explanation:

#"since there are 3 transformations label the endpoints"#

#A(2,3)" and "B(1,2)#

#color(blue)"first transformation"#

#"Under a rotation about the origin of "pi/2#

#• " a point "(x,y)to(-y,x)#

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

#rArrB(1,2)toB'(-2,1)#

#color(blue)"second transformation"#

#"under a translation "((0),(4))#

#• " a point "(x,y)to(x,y+4)#

#rArrA'(-3,2)toA''(-3,6)#

#rArrB'(-2,1)toB''(-2,5)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#rArrA''(-3,6)toA'''(-3,-6)#

#rArrB''(-2,5)toB'''(-2,-5)#

#"after all 3 transformations"#

#(2,3)to(-3,-6)" and "(1,2)to(-2,-5)#