Question

A line segment has endpoints at `(0 ,4 )` and `(1 , 8 )`. If the line segment is rotated about the origin by `pi /2`, translated horizontally by `5`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(-1,0)" and "(3,1)`

Explanation:

`"label the endpoints "A(0.4)" and "B(1,8)`

`color(blue)"First transformation"`

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

`• " a point "(x,y)to(-y,x)`

`A(0,4)toA'(-4,0)" and "B(1,8)toB'(-8,1)`

`color(blue)"Second transformation"`

`"under a translation "<5,0>`

`• " a point "(x,y)to(x+5,y)`

`A'(-4,0)toA''(1,0)" and "B'(-8,1)toB''(-3,1)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(-x,y)`

`rArrA''(1,0)toA'''(-1,0)`

`rArrB''(-3,1)toB'''(3,1)`

`"after all 3 transformations"`

`(0,4)to(-1,0)" and "(1,8)to(3,1)`