# A line segment has endpoints at #(0 ,4 )# and #(1 , 8 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 5 #, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 1 Answer

Nov 17, 2017

#### Explanation:

#"label the endpoints "A(0.4)" and "B(1,8)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(-y,x)#

#A(0,4)toA'(-4,0)" and "B(1,8)toB'(-8,1)#

#color(blue)"Second transformation"#

#"under a translation "<5,0>#

#• " a point "(x,y)to(x+5,y)#

#A'(-4,0)toA''(1,0)" and "B'(-8,1)toB''(-3,1)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#rArrA''(1,0)toA'''(-1,0)#

#rArrB''(-3,1)toB'''(3,1)#

#"after all 3 transformations"#

#(0,4)to(-1,0)" and "(1,8)to(3,1)#