A line segment has endpoints at (1 ,2 ) and (3 ,8 ). If the line segment is rotated about the origin by pi /2 , translated vertically by 1 , and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
May 16, 2018
Explanation:
"since there are 3 transformations to be performed"
"label the endpoints"
A(1,2)" and "B(3,8)
color(blue)"First transformation"
"under a rotation about the origin of "pi/2
• " a point "(x,y)to(-y,x)
rArrA(1.2)toA'(-2,1)
rArrB(3,8)toB'*-8,3)
color(blue)"Second transformation"
"under a vertical translation "((0),(1))
•" a point "(x,y)to(x,y+1)
rArrA'(-2,1)toA''(-2,2)
rArrB'(-8,3)toB''(-8,4)
color(blue)"Third transformation"
"under a reflection in the y-axis"
• " a point "(x,y)to(-x,y)
rArrA''(-2,2)toA'''(2,2)
rArrB''(-8,4)toB'''(8,4)
"After all 3 transformations"
(1,2)to(2,2)" and "(3,8)to(8,4)