Reflection Calculator

Enter a point's X and Y coordinates, choose your line of reflection (x-axis, y-axis, origin, y=x, or y=−x), and the Reflection Calculator returns the reflected point coordinates instantly. Perfect for geometry homework, coordinate plane practice, or verifying transformations across any standard axis or line. Also try the calculate New X Coordinate (x'), New Y Coordinate (y') & Type of Dilation — Dilation.

The x-coordinate of the original point P(x, y)

The y-coordinate of the original point P(x, y)

Choose the axis or line to reflect your point across

Results

Reflected Point P′

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Reflected X (x′)

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Reflected Y (y′)

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Distance from Reflection Line

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Reflection Rule Applied

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Frequently Asked Questions

What is a reflection in coordinate geometry?

A reflection is a transformation that creates a mirror image of a point or shape across a line called the line of reflection. Every point in the original figure is mapped to a corresponding point on the opposite side of the line, at an equal perpendicular distance. The result is a congruent image that appears 'flipped'. See also our Parallel Line Through a Point Calculator.

How do you reflect a point across the x-axis?

To reflect a point P(x, y) across the x-axis, keep the x-coordinate the same and negate the y-coordinate. The reflected point is P′(x, −y). For example, reflecting (3, 4) across the x-axis gives (3, −4).

How do you reflect a point across the y-axis?

Reflecting across the y-axis keeps the y-coordinate unchanged and negates the x-coordinate. The rule is P(x, y) → P′(−x, y). For example, (3, 4) becomes (−3, 4) after reflection over the y-axis.

What happens when you reflect a point through the origin?

Reflecting through the origin negates both coordinates: P(x, y) → P′(−x, −y). This is equivalent to a 180° rotation about the origin. For example, (3, 4) reflected through the origin gives (−3, −4). You might also find our Midpoint Calculator useful.

How do you reflect a point across the line y = x?

When reflecting across y = x, the x and y coordinates are simply swapped: P(x, y) → P′(y, x). So (3, 4) becomes (4, 3). This line acts as a diagonal mirror through the origin at a 45° angle.

How do you reflect a point across the line y = −x?

Reflecting across y = −x swaps the coordinates and negates both: P(x, y) → P′(−y, −x). For example, (3, 4) reflected across y = −x gives (−4, −3). This line runs diagonally through the origin in the opposite direction from y = x.

What is the distance from a point to its reflection?

The distance between an original point and its reflected image equals twice the perpendicular distance from the original point to the line of reflection. The midpoint of the segment connecting P and P′ always lies exactly on the line of reflection.

Can I reflect shapes (triangles, polygons) using this calculator?

This calculator reflects individual points. To reflect a triangle or polygon, apply the same reflection rule to each vertex separately, then connect the reflected vertices in the same order as the original shape. The reflected shape will be congruent to the original.