A line segment has endpoints at (8 ,5 ) and (2 ,1 ). If the line segment is rotated about the origin by ( 3 pi)/2 , translated horizontally by - 1 , and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Feb 28, 2018
Explanation:
"Since there are 3 transformations to be performed "
"label the endpoints"
A(8,5)" and "B(2,1)
color(blue)"First transformation"
"under a rotation about the origin of "(3pi)/2
• " a point "(x,y)to(y,-x)
rArrA(8,5)toA'(5,-8)
rArrB(2,1)toB'(1,-2)
color(blue)"Second transformation"
"under a translation "((-1),(0))
• " a point "(x,y)to(x-1,y)
rArrA'(5,-8)toA''(4,-8)
rArrB'(1,-2)toB''(0,-2)
color(blue)"Third transformation"
"under a reflection in the y-axis"
• " a point "(x,y)to(-x,y)
rArrA''(4,-8)toA'''(-4,-8)
rArrB''(0,-2)toB'''(0,-2)
"After all 3 transformations"
(8,5)to(-4,-8)" and "(2,1)to(0,-2)