Question

A line segment has endpoints at `(2 ,3 )` and `(2 ,1 )`. If the line segment is rotated about the origin by `( pi)/2`, translated vertically by `-8`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(-3,6)" and "(-1,6)`

Explanation:

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

`A=(2,3)" and "B=(2,1)`

`color(blue)"first transformation"`

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

`• " a point "(x,y)to(-y,x)`

`A(2,3)toA'(-3,2)`

`B(2,1)toB'(-1,2)`

`color(blue)"second transformation"`

`"under a vertical translation "((0),(-8))`

`• " a point "(x,y)to(x,y-8)`

`A'(-3,2)toA''(-3-6)`

`B'(-1,2)toB''(-1,-6)`

`color(blue)"third transformation"`

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

`• " a point "(x,y)to(x,-y)`

`A''(-3,-6)toA'''(-3,6)`

`B''(-1,-6)toB'''(-1,6)`

`"After all 3 transformations"`

`(2,3)to(-3,6)" and "(2,1)to(-1,6)`