Question

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

Answer 1

`(3,5)" and "(2,8)`

Explanation:

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

`"that is "A(2,3)" and "B(5,2)`

`color(blue)"First transformation"`

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

`• " a point "(x,y)to(-y,x)`

`rArrA(3,5)toA'(-3,2)`

`rArrB(5,2)toB'(-2,5)`

`color(blue)"Second transformation"`

`"under a translation "((0),(3))`

`• " a point "(x,y)to(x,y+3)`

`rArrA'(-3,2)toA''(-3,5)`

`rArrB'(-2,5)toB''(-2,8)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(-x,y)`

`rArrA''(-3,5)toA'''(3,5)`

`rArrB''(-2,8)toB'''(2,8)`

`"after all 3 transformations"`

`(2,3)to(3,5)" and "(5,2)to(2,8)`