Reflexão em Eixo X
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
reflexão em eixo x
About this calculator
The reflection calculator for the X axis transforms a point (x, y) in the Cartesian plane to its symmetric counterpart across the horizontal axis. The result is (x, -y), where the x-coordinate remains unchanged and the y-coordinate has its sign inverted. This operation is a fundamental linear transformation in linear algebra, represented by a diagonal matrix with elements 1 and -1.
Use this tool to quickly calculate or visualize the reflection of points, segments, or geometric figures. For example, reflecting a triangle with vertices at (1,2), (3,4), and (5,6) yields (1,-2), (3,-4), and (5,-6). Reflection is useful in computer graphics, physics (mirror symmetry), and analytic geometry problems.
Caution: reflection across the X axis does not change distances between points but reverses the orientation (clockwise/counterclockwise) of figures. Ensure the axis of reflection is indeed the X axis; for reflection across other axes, use specific calculators. The tool assumes real coordinates and does not handle special cases like points at infinity.
Frequently asked questions
What is reflection across the X axis?
It is a transformation that maps a point (x, y) to (x, -y), flipping the sign of the y-coordinate. This mirrors the point across the horizontal axis.
Does reflection across the X axis preserve distances?
Yes, the distance between two points is preserved because reflection is an isometry (distance-preserving transformation).
How to reflect an entire figure?
Apply the reflection to each vertex. For example, a square with vertices (1,1), (1,2), (2,2), (2,1) becomes (1,-1), (1,-2), (2,-2), (2,-1).
What is the difference between reflection across X axis and Y axis?
In X-axis reflection, the y-coordinate sign is flipped; in Y-axis reflection, the x-coordinate sign is flipped. They are distinct linear transformations.