Question

A line segment has endpoints at `(7 , 4)` and `(2 , 5)`. If the line segment is rotated about the origin by `(3pi)/2`, translated horizontally by `-3`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(-1,-7)" and "(-2,-2)`

Explanation:

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

`A=(7,4)" and "B=(2,5)`

`color(blue)"first transformation"`

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

`• " a point "(x,y)to(y,-x)`

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

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

`color(blue)"second transformation"`

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

`• " a point "(x,y)to(x-3,y)`

`A'(4,-7)toA''(1,-7)`

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

`color(blue)"third transformation"`

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

`• " a point "(x,y)to(-x,y)`

`A''(1,-7)toA'''(-1,-7)`

`B''(2,-2)toB'''(-2,-2)`

`"After all 3 transformations"`

`(7,4)to(-1,-7)" and "(2,5)to(-2,-2)`