When transforming points in a coordinate system, reflections across the axes and the origin produce specific results. Let's analyze the image of the point (2, 3) under the X-axis, Y-axis, and origin.
X-Axis Reflection
- The reflection of a point (x, y) across the X-axis changes the y-coordinate's sign while keeping the x-coordinate the same.
- For point (2, 3):
- The new point is (2, -3).
Y-Axis Reflection
- The reflection of a point (x, y) across the Y-axis changes the x-coordinate's sign while keeping the y-coordinate unchanged.
- For point (2, 3):
- The new point is (-2, 3).
Origin Reflection
- The reflection of a point (x, y) across the origin changes both the x and y coordinates' signs.
- For point (2, 3):
- The new point is (-2, -3).
In summary, the transformations yield the following results for the point (2, 3):
- X-axis reflection: (2, -3)
- Y-axis reflection: (-2, 3)
- Origin reflection: (-2, -3)
These transformations are essential in geometry for understanding symmetry and coordinate transformations.

X= 2and,y=3
x-axis=(2,0)
y-axis=(0,3)
origin=(0,0)