Mathematics Stack Exchange
Mathematics Stack Exchange

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.

561 questions
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Why does reflecting a point (x,y) about y=x result in point (y,x)?

I noticed that whenever reflecting a point (x,y) about the line y=x the x and y coordinates become swapped in order to give (y,x). However, I do not know why this is the case. Is there any way to geometrically/mathematically prove that this will…
1110101001
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Is it possible to reflect a linear equation across a curved equation?

I understand how to reflect equations across the x and y axises as well as the line y=x. But how do you reflect an equation across more complex equations such as other slant lines and higher order equations? Specifically I can easily reflect y=x^2…
El Zapatilla
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how to find the point obtained by reflecting over a line?

Given the point $A=(-2,6)$ and the line $y=2x$,what are the coordinates of the point B obtained by reflecting A over the line $y=2x$ ? Can someone teach me how to solve this question please?
c.chih
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Question about reflection, eight queens problem.

When I am to reflect a current chessboard around say the horizontal line Y=4, would that imply that I need to reflect the bottom part to the top part, and then the top part to the bottom part?
Algific
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Reflection of a curve/point using graph transformations.

The original question is to reflect the curve $y^2=4ax$ about the line $y+x=a$. The general method to solve such a question is to consider the parametric coordinates of the given curve (in this case $(at^2,2at)$) and reflect this general point about…
Aditya
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$A (3,1)$ reflected to $y=2x$ what is area of AOA'?

$y_1 = 2x$ = line of reflection $x_1,y_1 = A(3,1) =$ reflected point General formation of a line $y = mx + k$ $Ax + By + C = 0$ Finding a line perpendicular to line of reflection $m_2 = \frac{-1}{2}$ $y_2 = \frac{-1}{2}x + \frac{5}{2}$ Intersection…
Dini
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Raster scan with a rotating mirror

I'm trying to figure out a way to scan a 2D raster (like a TV or CRT monitor) with a beam using two rotating mirrors for the X and Y positions. I'm looking for a shape that will, when spinning, deflect a beam in discrete steps on one axis…
Yarek T
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How to reflect a point around a line in hexagonal coordinates

I have a hexagonal coordinate system. (If you'd like a better understanding of the coordinate system, I learned it from here) I would like to reflect points (hexagons) across given lines. In fact, the only lines I need to reflect across are those…
Pro Q
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Linearity of Certain Reflections in $\Bbb R^n$

Let $f: \mathbb{R^n} \rightarrow \mathbb{R^n}$ be a reflection about a hyperplane passing through $\vec 0$. Is $f$ always a linear transformation? If so, how can the matrix of the reflection be determined based what is known about the hyperplane?
FreshAir
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How to find the coordinates of the reflection of the point $(1, 0)$ in the line $y = mx$?

How to find the coordinates of the reflection of the point $(1, 0)$ in the line $y = mx$? I tried, but I can't think of any way to start this problem. Any help is greatly appreciated.
Eris Tyenns
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What is the image of a point without a defined line of reflection?

I have a problem: "A function $f$ is defined on the complex numbers by $f(z) = (a+bi)z$, where $a$ and $b$ are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the…
mpnm
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Reflection of light

There is a beam of light which strikes $BC$ at the point given in the diagram at an angle $\alpha = 19.94^{\circ}$ with $BC$ and reflects at an equal angle. The reflections continue following the law: $$\text{angle of incidence} = \text{angle of…
saisanjeev
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How do we find the co-ordinates of reflection point. And what's the logic behind?

The point R is the reflection of the point −1, 3 in the line 3y + 2x = 33. Find by calculation the coordinates of R.
Asad
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Cartesian plane question

In the Cartesian plane let $O(0,0)$ , $P(\cos A,\sin A)$, $Q( - \sin A , \cos A)$ be the vertices of a triangle. Two circles are drawn with $OP$, $OQ$ as diameter intersecting at $R$. Then find $OR$. I know that $Q$ is the reflection of $P$ in…
Yami Kanashi
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Find the reflection $f(x)$ and the invers reflection of$ f(x)$

With the given reflection \begin{align} f(7x-5)=2x-1 \end{align} How would I find this reflection, any orientation would be appreciated!
user397419
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