Question

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

Answer 1

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

Explanation:

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

`A(2,1)" and "B(0,5)`

`color(blue)"First transformation"`

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

`• " a point "(x,y)to(-y,x)`

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

`rArrB(0,5)toB'(-5,0)`

`color(blue)"Second transformation"`

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

`• " a point "(x,y)to(x+1,y)`

`rArrA'(-1,2)toA''(0,2)`

`rArrB'(-5,0)toB''(-4,0)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(x,-y)`

`rArrA''(0,2)toA'''(0,-2)`

`rArrB''(-4,0)toB'''(-4,0)`

`"after all 3 transformations"`

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