Question

A line segment has endpoints at `(3 , 2)` and `(1 ,3)`. If the line segment is rotated about the origin by `(3pi)/2`, translated horizontally by `-5`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

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

Explanation:

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

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

`color(blue)"first transformation"`

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

`• " a point "(x,y)to(y,-x)`

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

`rArrB(1,3)toB'(3,-1)`

`color(blue)"second transformation"`

`"under a translation " ((-5),(0))`

`• " a point "(x,y)to(x-5,y)`

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

`rArrB'(3,-1)toB''(-2,-1)`

`color(blue)"third transformation"`

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

`• " a point "(x,y)to(x,-y)`

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

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

`"under all 3 transformations"`

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