To find the ordered pair of \( X' \) after rotating the point \( X(3, 4) \) by \( 180^\circ \) around the origin, let's follow these steps:
1. Identify the original coordinates of the point \( X \):
- The original coordinates are \( (3, 4) \).
2. Understand the effect of a \( 180^\circ \) rotation around the origin:
- Rotating a point \( (x, y) \) by \( 180^\circ \) around the origin transforms the coordinates to \( (-x, -y) \).
3. Apply the transformation:
- For the point \( X(3, 4) \):
- The new \( x \)-coordinate will be \( -3 \) (since \( x = 3 \) and \( -x = -3 \)).
- The new \( y \)-coordinate will be \( -4 \) (since \( y = 4 \) and \( -y = -4 \)).
4. Write the new ordered pair \( X' \):
- The ordered pair after rotation is \( (-3, -4) \).
Therefore, the ordered pair of [tex]\( X' \)[/tex] after rotating point [tex]\( X(3, 4) \)[/tex] by [tex]\( 180^\circ \)[/tex] is [tex]\( \boxed{(-3, -4)} \)[/tex].
