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

##### 1 Answer

Jan 12, 2018

#### Explanation:

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

#"the endpoints"#

#"that is "A(2,3)" and "B(5,2)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(-y,x)#

#rArrA(3,5)toA'(-3,2)#

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

#color(blue)"Second transformation"#

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

#• " a point "(x,y)to(x,y+3)#

#rArrA'(-3,2)toA''(-3,5)#

#rArrB'(-2,5)toB''(-2,8)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#rArrA''(-3,5)toA'''(3,5)#

#rArrB''(-2,8)toB'''(2,8)#

#"after all 3 transformations"#

#(2,3)to(3,5)" and "(5,2)to(2,8)#