Question

Pentagon ABCDE is shown on the coordinate plane below:

Pentagon on coordinate plane with ordered pairs at A negative 2, 4, at B negative 6, 2, at C negative 5, negative 2, at D 1, negative 2, at E 2, 2.

If pentagon ABCDE is rotated 180° around the origin to create pentagon A′B′C′D′E′, what is the ordered pair of point C′?
(−5, 2)
(5, 2)
(2, −5)
(−2, 5)

Answer 1

To rotate a point \( (x, y) \) by 180° around the origin, the new coordinates \( (x', y') \) are given by:

\[
(x', y') = (-x, -y)
\]

For point C, the coordinates are \( C(-5, -2) \).

Applying the rotation:

\[
C' = (-(-5), -(-2)) = (5, 2)
\]

Thus, the ordered pair for point \( C' \) is \( (5, 2) \).

So the correct answer is:

\((5, 2)\)