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

Answer:

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

Step-by-step 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:

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