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

(-4,-8)" and "(0,-2)

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)