Question

The vertices triangle ABC are 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'. What are the coordinates of the vertices of A'B'C' ?

Answer 1

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 :

$(x,y)~~~\Rightarrow~~~(-x,-y).$

Therefore, the co-ordinates of the vertices of triangle A'B'C' are

$A(0,3)~~~\Rightarrow~~~A'(0,-3),\\\\B(2,-4)~~~\Rightarrow~~~B'(-2,4),\\\\C(-4,-6)~~~\Rightarrow~~~C'(4,6).$

Thus, the co-ordinates of the vertices of the triangle A'B'C are A'(0,-3), B'(-2, 4) and C'(4, 6).

Answer 2

work shown above! basically each coordinate is opposite so the new coordinates would be A(0,-3) B(-2,4) C(4,6)