Reflection Over Line Calculator
Reflect points across x-axis, y-axis, or y=x mirror lines.
Reflection Rules
x-axis: (x,y) → (x,-y) — negate y only
y-axis: (x,y) → (-x,y) — negate x only
y=x: (x,y) → (y,x) — swap x and y
Reflection Examples Table
| Original | x-axis | y-axis | y=x |
|---|---|---|---|
| (2,3) | (2,-3) | (-2,3) | (3,2) |
| (4,-1) | (4,1) | (-4,-1) | (-1,4) |
| (-3,2) | (-3,-2) | (3,2) | (2,-3) |
Frequently Asked Questions
What is reflection in geometry?
Reflection flips a point across a line (mirror line). The reflected point is equidistant from the line on the opposite side. All distances and angles are preserved (isometry).
What are the three common reflection lines?
x-axis: (x,y)→(x,-y). y-axis: (x,y)→(-x,y). y=x: (x,y)→(y,x). These are standard in coordinate geometry.
How do I reflect across the x-axis?
Keep x, negate y. Point (3,5)→(3,-5). Point flips vertically across the x-axis line.
How do I reflect across the y-axis?
Negate x, keep y. Point (3,5)→(-3,5). Point flips horizontally across the y-axis line.
How do I reflect across y=x?
Swap x and y. Point (3,5)→(5,3). Coordinates exchange positions.
Is distance preserved in reflection?
Yes. Reflection is an isometry. If points are 5 units apart, reflections are also 5 units apart.
Do angles stay the same after reflection?
Yes, angles are preserved. Triangles reflect to congruent triangles with same angles, sides scaled 1:1.
What happens to orientation in reflection?
Orientation reverses. Clockwise becomes counterclockwise. This orientation-reversing property distinguishes reflection from rotation.
How do I reflect a polygon?
Apply reflection rule to each vertex separately. Connect reflected vertices. Entire polygon reflects uniformly.
What is the line of reflection?
The line of reflection is the mirror. All original points and reflected points are equidistant from this line, at right angles.
Can I reflect across other lines like y=2x?
Yes, but requires complex calculations (rotation + reflection + translation). Standard geometry focuses on x-axis, y-axis, y=x.
How is reflection different from rotation?
Reflection: flips across line, reverses orientation. Rotation: turns around point, preserves orientation. Both preserve distances.