Question

A line segment has endpoints at `(7 ,9 )` and `(5 ,2)`. If the line segment is rotated about the origin by `pi`, translated vertically by `-4`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(-7,13)" and " (-5,6)`

Explanation:

Since there are 3 transformations to be performed, label the endpoints A(7 ,9) and B(5 ,2)

`color(blue)"first transformation" " Under a rotation about origin of " pi`

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

`"Hence "A(7,9)toA'(-7,-9)`

`"and " B(5,2)toB'(-5,-2)`

`color(blue)"Second transformation" " Under a translation " ((0),(-4))`

`"a point " (x,y)to(x,y-4)`

`"Hence " A'(-7,-9)toA''(-7,-13)`

`"and " B'(-5,-2)toB''(-5,-6)`

`color(blue)"third transformation"" Under a reflection in the x-axis"`

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

`"Hence " A''(-7,-13)toA'''(-7,13)`

`"and " B''(-5,-6)toB'''(-5,6)`

`"After all 3 transformations"`

`(7,9)to(-7,13)" and " (5,2)to(-5,6)`