How this calculator works
The signs of x and y identify a quadrant. Points on an axis do not belong to a quadrant. The shortest distance to the x axis is the magnitude of y, and the distance to the y axis is the magnitude of x. Reflections change the sign of the coordinate perpendicular to the mirror axis. This numeric tool does not draw a grid.
Formula
Reflection in x axis: (x, -y); in y axis: (-x, y); through origin: (-x, -y). Axis distances: |y| and |x|.
Worked example
The point (3, -4) is in quadrant IV. It is 4 units from the x axis and 3 units from the y axis. Reflection in the x axis gives (3, 4).
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Frequently asked questions
Where is quadrant I?
It is above the x axis and to the right of the y axis. Quadrants are numbered anticlockwise.
Is the origin in every quadrant?
No. It is the intersection of the two axes and lies in no quadrant.
Does reflecting change distances?
Reflection preserves lengths. It changes the position and orientation relative to the chosen mirror.