Rectangle ABCD is rotated 180°. What rule shows the input and output of the rotation, and what is the new coordinate of A′?

A' (-1, 3)

Step-by-step explanation:

A shape has symmetry if we are unable to distinguish it from its transformed image. A shape has rotation symmetry if there exists a rotation less than 360° that carries the shape onto itself. Which means that if you can rotate a shape less than 360° about some point and the shape looks like it never moved, it has rotation symmetry.

A rectangle is an example of rotation symmetry because if we rotate a rectangle at 180° about its center, it looks exactly the same. However, the points diagonal with each other are exchanged.

So, when the given rectangle is rotated 180° , the tranformed rectangle has the point A' at the same location of point C of the orginal shape.

So coordinates of A' are (-1, 3)

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)