Question

A line segment has endpoints at `(8 ,5 )` and `(2 ,1 )`. If the line segment is rotated about the origin by `( 3 pi)/2`, translated horizontally by `- 1`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(-4,-8)" and "(0,-2)`

Explanation:

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

`A(8,5)" and "B(2,1)`

`color(blue)"First transformation"`

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

`• " a point "(x,y)to(y,-x)`

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

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

`color(blue)"Second transformation"`

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

`• " a point "(x,y)to(x-1,y)`

`rArrA'(5,-8)toA''(4,-8)`

`rArrB'(1,-2)toB''(0,-2)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(-x,y)`

`rArrA''(4,-8)toA'''(-4,-8)`

`rArrB''(0,-2)toB'''(0,-2)`

`"After all 3 transformations"`

`(8,5)to(-4,-8)" and "(2,1)to(0,-2)`