Question

Pentagon ABCDE is shown on the coordinate plane below:

Pentagon on coordinate plane with ordered pairs at A (-2, 4), at B (-6, 2), at C (-5, -2), at D (1, ?)
If pentagon ABCDE is rotated 180° around the origin to create pentagon A'B'C'D'E', what is the ordered pair of point D'?
a) (−1, 2)
b) (2, 1)
c) (1, −2)
d) (−2, −1)

Answer 1

The ordered pair of point D' after a 180° rotation around the origin is (−1, 2), as it is the only option with a negated x-coordinate and a positive y-coordinate.

Step-by-step explanation:

When a point on the coordinate plane is rotated 180° around the origin, both the x and y coordinates of the point are negated. This means if we have a point D with coordinates (1, ?), after the rotation, the new point D' will have coordinates (-1, -?). Unfortunately, the value for the y-coordinate of point D is not provided in the question. However, based on the choices provided, we can determine that the correct y-coordinate of D' must be positive since rotating 180° around the origin negates the y-coordinate.

Considering the options provided, only option a) (−1, 2), would be the proper coordinate after such a rotation because it is the only option with a negated x-coordinate and a positive y-coordinate. Therefore, the ordered pair of point D' after a 180° rotation around the origin is (−1, 2).