# Questions tagged [reflection]

Reflection is a transformation that fixes a line or plane or a more general subset. Reflections appear in geometry, linear algebra, complex analysis, differential equations, etc -- therefore, this tag must be used with a tag describing the area of mathematics.

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### Finite cyclic groups are reflection groups.

I am following a note on complex reflections. There the notion of pseudoreflection groups are introduced. A pseuforeflection $\sigma : \mathbb C^n \longrightarrow \mathbb C^n$ is a linear isomorphism ...
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### Proving two circles are concentric given some conditions involving an isosceles trapezium and reflections.

In an isosceles trapezoid, $ABCD$ ($AB ∥ CD$) points $E$ and $F$ lie on the segment $CD$ in such a way that $D$, $E$, $F$, and $C$ are in that order, and $DE = CF$. Let $X$ and $Y$ be the reflection ...
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### Finding the plane curve resulting from a reflection onto another plane curve

Question: What is the best way to describe the set of reflected points of one plane curve along the perpendicular lines at points of another plane curve? I am trying to find a way to find the ...
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### Find two ratios given an inequality about a triangle with integer coordinates

Let $A(0,0)$, $B(p,q)$, $C(r,s)$ where $p,q,r,s \in \mathbb{Z}$. Also, it is known that $(|AB|+|BC|)^2<8\cdot \textbf{Area}(\triangle{ABC})+1$ $1.$ If $\triangle{ABC}$ is reflected across side $AC$...
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### Multiple reflections and determinant

If a linear transformation swaps two axes is said to perform a reflection and the determinant will be negative. Testing for the sign of the determinant can tell me whether a reflection has happened. ...
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