Question

A line segment has endpoints at `(7 ,9 )` and `(3 ,6 )`. 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

`(-9,-3)" and "(-6,1)`

Explanation:

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

`rArrA(7,9)" and "B(3,6)`

`color(blue)"First transformation"`

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

`• " a point "(x,y)to(y,-x)`

`rArrA(7,9)toA'(9,-7)`

`rArrB(3,6)toB'(6,-3)`

`color(blue)"Second transformation"`

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

`• " a point "(x,y)to(x,y+4)`

`rArrA'(9,-7)toA''(9,-3)`

`rArrB'(6,-3)toB''(6,1)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(-x,y)`

`rArrA''(9,-3)toA'''(-9,-3)`

`rArrB''(6,1)toB'''(-6,1)`

`"after all 3 transformations"`

`(7,9)to(-9,-3)" and "(3,6)to(-6,1)`