Rectangle abcd is reflected over the y-axis. what rule shows the input and output of the reflection, and what is the new coordinate of a'?

Solution:

As given Rectangle ABCD is reflected over the y- axis.

When a shape or geometrical figure is reflected through a line it's distance that is distance of image from line and distance of Pre-image from that line is always same.Also perpendicular distance of vertices of any polygon that is considered for reflection has same distance from that line after reflection and before reflection.

Suppose the coordinate of A be (x,y) and considering Rectangle A B CD lie in first quadrant then when it is reflected through y - axis that is through the line x=0, it's new coordinate will become A' (-x,y).

If rectangle is in second quadrant having Vertices that is vertices of A (-x,y) then reflected over line that is x=0,→ y axis then Vertices of A' (x,y).

If rectangle is in third quadrant having Vertices that is vertices of A (-x,-y) then reflected over line that is x=0,→ y axis then Vertices of A' (x,-y).

If rectangle is in fourth quadrant having Vertices that is vertices of A (x,-y) then reflected over line that is x=0,→y axis then Vertices of A' (-x,-y).

the answer is simply just 6n add the two together as they have an n