Question

A line segment has endpoints at `(7 ,2 )` and `(3 , 2 )`. If the line segment is rotated about the origin by `(3 pi ) /2`, translated horizontally by `5`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(-7,-7)" and "(-7,-3)`

Explanation:

`"since there are 3 transformations to be performed"`
`"label the endpoints"`

`A(7,2)" and "B(3,2)`

`color(blue)"First transformation"`

`"under a rotation about the origin of "(3pi)/2`

`• " a point "(x,y)to(y,-x)`

`rArrA(7,2)toA'(2,-7)`

`rArrB(3,2)toB'(2,-3)`

`color(blue)"Second transformation"`

`"under a translation "((5),(0))`

`• " a point "(x,y)to(x+5,y)`

`rArrA'(2,-7)toA''(7,-7)`

`rArrB'(2,-3)toB''(7,-3)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(-x,y)`

`rArrA''(7,-7)toA'''(-7,-7)`

`rArrB''(7,-3)toB'''(-7,-3)`

`"After all 3 transformations"`

`(7,2)to(-7,-7)" and "(3,2)to(-7,-3)`