Question

A line segment has endpoints at `(7 ,4 )` and `(2 ,6)`. If the line segment is rotated about the origin by `(3pi )/2`, translated vertically by `3`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(4,4)" and "(6,-1)`

Explanation:

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

`A(7,4)" and "B(2,6)`

`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(2,6)toB'(6,-2)`

`color(blue)"Second transformation"`

`"under a translation "((0),(3))`

`• " a point "(x,y)to(x,y+3)`

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

`rArrB'(6,-2)toB''(6,1)`

`color(blue)"Third transformation"`

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

`• " a point "(x,y)to(x,-y)`

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

`rArrB''(6,1)toB'''(6,-1)`

`"after all 3 transformations"`

`(7,4)to(4,4)" and "(2,6)to(6,-1)`