Question

A line segment has endpoints at `(4 ,9 )` and `(2 ,7 )`. 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

`(-9,4)" and "(-7,6)`

Explanation:

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

`A=(4,9)" and "B=(2,7)`

`color(blue)"first transformation"`

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

`• " a point "(x,y)to(-y,x)`

`A(4,9)toA'(-9,4)`

`B(2,7)toB'(-7,2)`

`color(blue)"second transformation"`

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

`• " a point "(x,y)to(x,y-8)`

`A'(-9,4)toA''(-9,-4)`

`B'(-7,2)toB''(-7,-6)`

`color(blue)"third transformation"`

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

`• " a point "(x,y)to(x,-y)`

`A''(-9,-4)toA'''(-9,4)`

`B''(-7,-6)toB'''(-7,6)`

`"After all 3 transformations"`

`(4,9)to(-9,4)" and "(2,7)to(-7,6)`