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

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

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)