Question

A line segment has endpoints at `(7 ,2 )` and `(3 ,4 )`. If the line segment is rotated about the origin by `(3 pi)/2`, translated vertically by `4`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(-2,-3)" and "(-4,1)`

Explanation:

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

`A=(7,2)" and "B=(3,4)`

`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(3,4)toB'(4,-3)`

`color(blue)"Second transformation"`

`"under a vertical translation "((0),(4))`

`• " a point "(x,y)to(x,y+4)`

`rArrA'(2,-7)toA''(2,-3)`

`rArrB'(4,-3)toB''(4,1)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(-x,y)`

`rArrA''(2,-3)toA'''(-2,-3)`

`rArrB''(4,1)toB'''(-4,1)`

`"After all 3 transformations"`

`(7,2)to(-2,-3)" and "(3,4)to(-4,1)`