Question

A line segment has endpoints at `(3 , 1)` and `(2 ,3)`. If the line segment is rotated about the origin by `(3pi)/2`, translated horizontally by `7`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(8,3)" and " (10,2)`

Explanation:

`"label the endpoints " A(3,1)" and " B(2,3)`

`color(blue)"First transformation "" under a rotation about O of " (3pi)/2`

`"a point " (x,y)to(y,-x)`

`rArrA(3,1)toA'(1,-3)" and " B(2,3)toB'(3,-2)`

`color(blue)"Second transformation"" under a translation " ((7),(0))`

`"a point " (x,y)to(x+7,y)" hence"`

`A'(1,-3)toA''(8,-3),B'(3,-2)toB''(10,-2)`

`color(blue)"Third transformation"" reflection in x-axis"`

`"a point " (x,y)to(x,-y)" hence"`

`A''(8,-3)toA'''(8,3),B''(10,-2)toB'''(10,2)`

`"After all 3 transformations"`

`(3,1)to(8,3)" and " (2,3)to(10,2)`