Rectangle EFGH is rotated 180° around point O.What are the coordinates of G’?G’(–2, –2)G’(–4,–2)G’(2, –4)→→G’(4, 2)←←Answer is D :)

Rotation is a given a rigid motion or transformation which refers to movement of a figure around a center of rotation. 

In this exercise is given the points representing the vertices of a rectangle and it is asked to find its new coordinates after a rotation of 180° about the origin, which means a rotation in the direction the hands of a clock rotate or move.

In this exercise it is asked to find the coordinates of the new vertices after the 180 degrees rotation, which is define or represented by the rule (x,y)--(-x,-y).

To find the vertices of the image rectangle, you should substitute the points of the pre-image into the previous mention rule.

Pre-Image          Image
 E(-2,1) ----------  E'(2,-1) 
 F(-4,1) ----------  F'(4,-1)
 G(-4,-2) ---------  G'(4,2)
 H(-2,-2) ---------  H'(2,2)

The coordinate of point G after a rotation of 180° is (4,2).