Answer: The co-ordinates of the vertices of the triangle A'B'C are A'(0,-3), B'(-2, 4) and C'(4, 6).
Step-by-step explanation: Given that the vertices of triangle ABC A(0,3), B(2,-4) and C(-4,-6). Triangle ABC is rotated 180 degrees counter close wise about the origin to form A'B'C'.
We are to find the co-ordinates of the vertices of triangle A'B'C'.
We know that
if a point (x, y) is rotated 180 degrees counterclockwise about the origin, then its co-ordinates changes as follows :
[tex](x,y)~~~\Rightarrow~~~(-x,-y).[/tex]
Therefore, the co-ordinates of the vertices of triangle A'B'C' are
[tex]A(0,3)~~~\Rightarrow~~~A'(0,-3),\\\\B(2,-4)~~~\Rightarrow~~~B'(-2,4),\\\\C(-4,-6)~~~\Rightarrow~~~C'(4,6).[/tex]
Thus, the co-ordinates of the vertices of the triangle A'B'C are A'(0,-3), B'(-2, 4) and C'(4, 6).
