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)

 The correct option is (B) (5, 2).

Step-by-step explanation:  Given that the co-ordinates of the vertices of pentagon ABCDE are A(-2, 4), B(-6, 2), C(-5, -2), D(1, -2) and E(2, 2).

We are to find the co-ordinates of the point C', if the pentagon ABCDE is  rotated 180° around the origin to create pentagon A'B'C'D'E'.

We know that a rotation of 180° changes the co-ordinates of a point (x, y) according to the following rule:

(x, y)  ⇒  (-x, -y).

Therefore, the vertices of pentagon ABCD will transform to the vertices of pentagon A'B'C'D'E' as follows:

A(-2, 4)  ⇒ A'(2, -4),

B(-6, 2)   ⇒ B'(6, -2),

C(-5, -2)  ⇒  C'(5, 2),

D(1, -2)    ⇒  D'(-1, 2),

E(2, 2)    ⇒   E'(-2, -2).

Thus, the co-ordinates of the point C' are (5, 2).

Option (B) is correct.

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step-by-step explanation: