Question

A line segment has endpoints at `(7 ,5 )` and `(6 ,5)`. If the line segment is rotated about the origin by `(3pi )/2`, translated vertically by `3`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(5,4)" and "(5,3)`

Explanation:

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

`A=(7,5)" and "B=(6,5)`

`color(blue)"first transformation"`

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

`• " a point "(x,y)to(y,-x)`

`A(7,5)toA'(5,-7)`

`B(6,5)toB'(5,-6)`

`color(blue)"second transformation"`

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

`• " a point "(x,y)to(x,y+3)`

`A'(5,-7)toA''(5,-4)`

`B'(5,-6)toB''(5,-3)`

`color(blue)"third transformation"`

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

`• " a point "(x,y)to(x,-y)`

`A''(5,-4)toA'''(5,4)`

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

`"After all 3 transformations"`

`(7,5)to(5,4)" and "(6,5)to(5,3)`