Question

A line segment has endpoints at `(2 , 3)` and `(1 , 2)`. If the line segment is rotated about the origin by `(pi)/2`, translated vertically by `4`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(-3,-6)" and "(-2,-5)`

Explanation:

`"since there are 3 transformations label the endpoints"`

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

`color(blue)"first transformation"`

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

`• " a point "(x,y)to(-y,x)`

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

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

`color(blue)"second transformation"`

`"under a translation "((0),(4))`

`• " a point "(x,y)to(x,y+4)`

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

`rArrB'(-2,1)toB''(-2,5)`

`color(blue)"third transformation"`

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

`• " a point "(x,y)to(x,-y)`

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

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

`"after all 3 transformations"`

`(2,3)to(-3,-6)" and "(1,2)to(-2,-5)`