Let's Check In If \( P^{\prime}(-1,-3) \) is obtained by a \( 180^{\circ} \mathrm{ccw} \) rotation about the origin what are the coordinates of \( P \) ? A. \( (1,-3) \) B. \( (1,3) \) C. \( (-1,3) \) D. \( (-1,-3) \) Please select the best answer from the choices provided A A B O C

To find the coordinates of point \( P \) before the \( 180^{\circ} \) counterclockwise rotation around the origin, we can use the fact that a \( 180^{\circ} \) rotation transforms any point \( (x, y) \) to \( (-x, -y) \). Given the point \( P'(-1, -3) \) after rotation, we can reverse the transformation. So, the original point \( P \) will be \( (1, 3) \). That means the correct answer is B. It’s important to remember that a \( 180^{\circ} \) rotation flips the signs of both coordinates. This principle simplifies many geometry problems and can be particularly fun to visualize on a graph! In real-world applications, understanding rotations isn’t just for math class. It’s the basis of computer graphics, robotics, and animation! Knowing how points move in two-dimensional space helps designers create realistic simulations and games. So next time you see a character spin in a video game, remember—there’s some geometrical magic behind it!