Question

A line segment has endpoints at `(7 ,5 )` and `(8 ,2 )`. If the line segment is rotated about the origin by `pi`, translated horizontally by `- 1`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(-8,5)" and "(-9,2)`

Explanation:

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

`A=(7,5)" and "B=(8,2)`

`color(blue)"first transformation"`

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

`• " a point "(x,y)to(-x,-y)`

`A(7,5)toA'(-7,-5)`

`B(8,2)toB'(-8,-2)`

`color(blue)"second transformation"`

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

`• " a point "(x,y)to(x-1,y)`

`A'(-7,-5)toA''(-8,-5)`

`B'(-8,-2)toB''(-9,-2)`

`color(blue)"third transformation"`

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

`• " a point " (x,y)to(x,-y)`

`A''(-8,-5)toA'''(-8,5)`

`B''(-9,-2)toB'''(-9,2)`

`"After all 3 transformations"`

`(7,5)to(-8,5)" and "(8,2)to(-9,2)`