Question

A line segment has endpoints at `(6 ,2 )` and `(3 ,7)`. 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

`(2,7)" and "(7,4)`

Explanation:

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

`A(6,2)" and "B=(3,7)`

`color(blue)"first transformation"`

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

`• " a point "(x,y)to(-y,x)`

`A(6,2)toA'(-2,6)`

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

`color(blue)"second transformation"`

`"under a vertical translation "((0),(1))`

`• " a point "(x,y)to(x,y+1)`

`A'(-2,6)toA''(-2,7)`

`B'(-7,3)toB''(-7,4)`

`color(blue)"third transformation"`

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

`• " a point "(x,y)to(-x,y)`

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

`B''(-7,4)toB'''(7,4)`

`"After all 3 transformations"`

`(6,2)to(2,7)" and "(3,7)to(7,4)`