Question

A rectangle with the vertices (3, -2), (3, -4), (7, -2), (7, -4) is reflected across the x-axis and the rotated 90 degrees counter clockwise

Answer 1

The new vertices are:
`(-2,3),(-4,3),(-2,7),(-4,7)`

Explanation:

The given vertices are
`(3,-2),(3,-4),(7,-2),(7,-4)`

Rule for reflection about x axis is
`(x,y)`→
`(x,-y)`.

So,
`(3,-2)`→
`(3,2)`

`(3,-4)`→
`(3,4)`

`(7,-2)`→
`(7,2)`

`(7,-4)`→
`(7,4)`

Now, new vertices after reflection about x axis are
`(3,2),(3,4),(7,2),(7,4)`.

Rule for 90 degree rotation counter-clockwise is
`(x,y)`→
`(-y,x)`.

So,
`(3,2)`→
`(-2,3)`

`(3,4)`→
`(-4,3)`

`(7,2)`→
`(-2,7)`

`(7,4)`→
`(-4,7)`

Therefore, the new rectangle after reflection about x axis and rotated 90 degrees counter-clockwise has the following vertices:

`(-2,3),(-4,3),(-2,7),(-4,7)`