Question

A line segment has endpoints at `(3 ,7 )` and `(4 ,5)`. 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?

Answer 1

`(7,2)" and " (5,3)`

Explanation:

`"since there are 3 transformations to be performed"`

`"label the endpoints " A(3,7)" and " B(4,5)`

`color(blue)"First transformation"`

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

`• " a point "(x,y)to(-y,x)`

`rArrA(3,7)toA'(-7,3),B(4,5)toB'(-5,4)`

`color(blue)"Second transformation"`

`"under a translation of "((0),(-1))`

`• " a point "(x,y)to(x,y-1)`

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

`rArrB'(-5,4)toB''(-5,3)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(-x,y)`

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

`rArrB''(-5,3)toB'''(5,3)`

`"after all 3 transformations"`

`(3,7)to(7,2)" and " (4,5)to(5,3)`