# Rotating Objects 180 Degrees Around The Origin

Review a quick way to rotate an object 180 degrees around the coordinate plane.

To rotate a triangle $$\text{ABC}$$ by 180 degrees around the origin, you need to perform the following steps:

1. Identify the Original Coordinates
$$A(-4,1)$$
$$B(-4,5)$$
$$C(-2,1)$$

2. Find the New Coordinates after Rotation
To rotate a point $$(x, y)$$ by 180 degrees around the origin, you simply negate both $$x$$ and $$y$$ to find the new coordinates: $$(-x, -y)$$.

3. Apply the Rotation to Each Vertex
For point $$A(-4,1)$$:
$$A'(-(-4), -1) = (4, -1)$$
For point $$B(-4,5)$$:
$$B'(-(-4), -5) = (4, -5)$$
For point $$C(-2,1)$$:
$$C'(-(-2), -1) = (2, -1)$$

4. Plot the New Triangle
Plot the points $$A'(4, -1)$$, $$B'(4, -5)$$, and $$C'(2, -1)$$ on the coordinate plane to form the rotated triangle.

5. Connect the Points
Connect the points $$A'$$, $$B'$$, and $$C'$$ to form the rotated triangle $$A'B'C'$$.

6. Verify the Rotation
Check if the new triangle $$A'B'C'$$ is rotated 180 degrees around the origin from the original triangle $$ABC$$.

In summary, to rotate triangle $$ABC$$ 180 degrees around the origin:
Point $$A(-4,1)$$ becomes $$A'(4, -1)$$.
Point $$B(-4,5)$$ becomes $$B'(4, -5)$$.
Point $$C(-2,1)$$ becomes $$C'(2, -1)$$.