Question

A line segment has endpoints at `(7 ,4 )` and `(5 ,2)`. If the line segment is rotated about the origin by `(3pi )/2`, translated vertically by `5`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

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

Explanation:

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

`A(7,4)" and "B(5,2)`

`color(blue)"First transformation"`

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

`• " a point "(x,y)to(y,-x)`

`rArrA(7,4)toA'(4,-7)`

`rArrB(5,2)toB'(2,-5)`

`color(blue)" Second transformation"`

`"under a translation "((0),(5))`

`• " a point "(x,y)to(x,y+5)`

`rArrA'(4,-7)toA''(4,-2)`

`rArrB'(2,-5)toB''(2,0)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(x,-y)`

`rArrA''(4,-2)toA'''(4,2)`

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

`"After all 3 transformations"`

`(7,4)to(4,2)" and "(5,2)to(2,0)`