Question

A line segment has endpoints at `(9 ,1 )` and `(5 ,3)`. If the line segment is rotated about the origin by `pi`, translated vertically by `-1`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(-9,2)" and "(-5,4)`

Explanation:

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

`A(9,1)" and "B(5,3)`

`color(blue)"First transformation"`

`"under a rotation about the origin by "pi`

`• " a point "(x,y)to(-x,-y)`

`rArrA(9,1)toA'(-9,-1)`

`rArrB(5,3)toB'(-5,-3)`

`color(blue)"Second transformation"`

`"under a translation "((0),(-1))`

`• " a point "(x,y)to(x,y-1)`

`rArrA'(-9,-1)toA''(-9,-2)`

`rArrB'(-5,-3)toB''(-5,-4)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(x,-y)`

`rArrA''(-9,-2)toA'''(-9,2)`

`rArrB''(-5,-4)toB'''(-5,4)`

`"After all 3 transformations"`

`(9,1)to(-9,2)" and "(5,3)to(-5,4)`