Question

Quadrilateral DEFG is rotated 180° about the origin to create quadrilateral D'E'F'G'. In which quadrant does G' lie?

Answer 1

Rotation in mathematics involves movement of a figure along a given point and a given angle. It is described by giving a the center of rotation and the angle of rotation, the angle indicates the direction of rotation whether clockwise or anticlockwise, such that if the angle is positive then the rotation is to the anticlockwise direction and if the angle is negative then the direction of rotation is clockwise. In our case the center of rotation is origin (0,0) and the angle of rotation is +180 degrees thus the direction of rotation is anticlockwise. Therefore if an object DEFG is rotated to an image D'E'F'G' , assuming point G was in the first quadrant then its image G' will fall on the third quadrant of the Cartesian plane.