# A line segment has endpoints at #(5 , 8)# and #(6 , 1)#. If the line segment is rotated about the origin by #pi/2 #, translated vertically by #-2#, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 2 Answers

Rule for Rotation by

Rule for Translated Vertically by

Rule for Reflection across y-axis

In that same order:

To Check, each of these transformations are isometric which means the distance between the points will not change.

Original Points

New Points

They have the same distance so the segment endpoints are correct.

#### Explanation:

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

#"label the endpoints"#

#A=(5,8)" and "B=(6,1)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-y,x)#

#rArrA(5,8)toA'(-8,5)#

#rArrB(6,1)toB'(-1,6)#

#color(blue)"second transformation"#

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

#• " a point "(x,y)to(x,y-2)#

#rArrA'(-8,5)toA''(-8,3)#

#rArrB'(-1,6)toB''(-1,4)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#rArrA''(-8,3)toA'''(8,3)#

#rArrB''(-1,4)toB'''(1,4)#

#"After all 3 transformations"#

#(5,8)to(8,3)" and "(6,1)to(1,4)#