Question

The vertices of /ABC are A(0, 3), B(2, –4), and C(–4, –6). /ABC is rotated 180° counterclockwise about the origin to form /A'B'C'. What are the coordinates of the vertices of /A'B'C'?
A.
A’(–3, 0), B’(4, –2), C’(6, 4)

B.
A’(0, –3), B’(–2, –4), C’(4, –6)

C.
A’(0, –3), B’(–2, 4), C’(4, 6)

D.
A’(3, 0), B’(4, 2), C’(–6, 4)

Answer 1

A'(-3,0)

B'(4,2)

C'(6,4)

Answer 2

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

On this problem is given that the points representing the vertices of a triangle were rotated by a 180 degree counterclockwise rotation, which means a rotation on the opposite direction that 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 counterclockwise rotation, which is define by the rule
(x,y)--(-x,-y)

To find the vertices of the image triangle, you should substitute the points of the preimage into the previous mention rule.

Pre-image             Image
A(0,3)          ---       A'(0,-3)
B(2,-4)         ---       B'(-2,4)
C(-4,-6)        ---      C'(4,6)

The coordinates of the vertices of triangle A'B'C' are (0,-3), (-2,4), and (4,6) or in other words letter C from the choices given.