Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

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2
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1answer
79 views

How do I calculate a point's coordinates on a circle’s circumference

I have got a circle with radius $r$ and center point $c_x$ and $c_y$. Known values: - $c_x$ and $c_y$ - $r$ - length $AR_a$ - length $BR_b$ Angle between point $A$ and the radius $r$ is unknown ...
2
votes
1answer
32 views

A coordinate geometry question.

On pg. 46 of "Coordinate geometry" by S.L. Loney, the following question has been posed: Show that the equations to the straight lines passing through the point $(3,-2)$ and inclined at $60^\circ$ ...
-2
votes
1answer
29 views

Distance to the point of intersection of two altitudes in a triangle

Problem $P,Q,R$ are the points $(4,2)$, $(2,1)$ and $(6,-3)$. Also, $PS$ and $QT$ are altitudes in this triangle. A) Find the equations of PS and QT My answer: PS: $y-x-2=0$, QT: $5y-2x-1=0$ ...
0
votes
0answers
36 views

Looking for certain functions or a coordinate transform respectively

I want to generate an image of the mandelbrot set. That means to map the x-y-coordinate-system, where the mandelbrot set lives (e.g. x:-2 .. 1; y:-1.5 .. 1.5) to an screen coordinate-system u-v (say ...
1
vote
0answers
102 views

Change of basis matrix notation confusion

I've got strange notation of change of basis matrix in my book and I'd like to have it explained a little bit. It says, if: $M _{\mathcal A}^{\mathcal B}(id) \cdot \vec{v} _{\mathcal B} = ...
0
votes
1answer
106 views

Finding the coordinates of a point in a given rectangle

I'm working on a computer program that displays on a screen that is 1280x800 pixels. I have a point that exists within the coordinates of the screen at the middle/origin. That gives me a view of 400 ...
1
vote
1answer
29 views

A rectangle $OACB$ with two axes as two sides,the origin $O$ as a vertex is drawn in which the length $OA$ is four times the width $OB$…

A rectangle $OACB$ with two axes as two sides,the origin $O$ as a vertex is drawn in which the length $OA$ is four times the width $OB$.A circle is drawn passing through the points BC and touching ...
1
vote
1answer
38 views

Deriving Cartesian Coordinates from Cylindrical Coordinates

The ans given was: $x = r \cos (\alpha)$ $y = h$ $z = -r \sin(\alpha)$ Could somebody explain to me how to arrive at the formula? I'm probably confused with the axes because usually, the $Z$ ...
1
vote
0answers
188 views

Reverse rotation back to original coordinates (Euler Angles)

so in the program I'm trying to write (still, it's a mathematical question) I have a set of coordinates and angles (Euler angles) which represent the place and orientation of an object in space, ...
0
votes
1answer
32 views

Determining whether a 3-dimensional equations creates a horizontal or non-horizontal plane?

I am learning about graphing 3-dimensional shapes on x,y,z coordinates axis and am understanding everything for the most part. However, the thing that is continuously tripping me up is distinguishing ...
1
vote
2answers
53 views

Coordinates rotation by $120$ degree

If I have a point on a standard grid with coordinates say: $A_1=(1000,0)$ $A_2=(707,707)$ Is there a easy way to transfer this points to $\pm 120$ degrees from the origin $(0,0)$, and ...
0
votes
1answer
92 views

How to calculate the points of the triangles making up an Octahedron?

Ok guys, I'm not a great mathematician but will try to work this as accurately as I can. I hope someone can help me. I am drawing some 3D objects and I am having trouble drawing an Octahedron. I ...
0
votes
0answers
52 views

Derivative in non orthogonal coordinates

I am trying to transform irregular shape in common Cartesian coordinates ($x-y$) into a regular shape in a generalized coordinates(e.g.,$u-v$), in which the transform can be defined as $u=u(x,y)$ and ...
2
votes
2answers
84 views

Graph of Sin(x) along the line y=x

Well, I want the equation of $\sin(x)$ which has the line $y=x$ as it's axis. Basically I want the $\frac\pi4$ rotation of the curve y=$\sin(x)$. I already attempted differentiating the curve and ...
2
votes
0answers
79 views

Get 2D coordinate transformation matrix based on points in a system and their angles in the other?

I'd like to get the parameters (rotation angle,$\Theta$, and translation coefficients, $x_0$ and $y_0$)) of a transformation for translating and rotating points in a coordinate system to another. As ...
5
votes
1answer
174 views

Jacobian of Fourier Transformation

I am trying to calculate the Jacobian determinate of the Fourier transform which I stumbled upon when studying the Path Integral in Quantum Field Theory. I know the answer should be $1$ but I don't ...
0
votes
1answer
59 views

Rolling of a circle along the positive $x$-axis without slipping and finding the locus of a point lying on the circumference of the circle.

Consider the circle of radius $1$ with its centre at the point $(0,1)$. From this initial position, the circle is rolled along the positive $x$-axis without slipping. Find the locus of the point $P$ ...
0
votes
1answer
280 views

coordinate geometry - find point in right-angled triangle

I'm making a map. I've come across a geometry problem, and I'm not so knowledgeable about maths! Let me illustrate with pictures. I am trying to plot flightpaths with a curved line, using a ...
0
votes
1answer
83 views

Great circle and how to “imagine” it in this case?

I am currently working on a riddle. I have to search and locate a person, but I do not know, where he is. I only have some informations, concerning the probability where he might be. A satellite ...
1
vote
1answer
61 views

Linear Algebra Coordinate Systems

Hi I have a few questions for you guys. I know that every change of coordinate matrix is invertible is true. Is the converse of this statement also true? Every invertible matrix is a ...
2
votes
3answers
83 views

To prove that the centre of 2 circles and the two points at which the 2 circles cut and the origin lie on a circle.

Let the circles $$x^2+y^2-2cy-a^2=0~~~~and~~~~x^2+y^2-2bx+a^2=0$$ with centres at $A$ and $B$ intersect at $P$ and $Q$. Show that the points $A,B,P,Q$ and $O=(0,0)$ lie on a circle. My work: I ...
1
vote
1answer
105 views

Find fourth coordinates given other three points

Find coordinates of $D$, given coordinates of $A,B,C$, torsion angle and angle between $BCD$. Is there any other way other than the torsion angle equation, $$n_1=⟨b_1\times b_2⟩ \;\text{ and }\; ...
0
votes
2answers
75 views

How to find the x-component of a spherical vector?

I am given the point $P(r=0.89, \theta=30^\omicron, \phi=45^\omicron)$ and $\vec E=1/r^2(cos(\phi)\hat a_r +sin(\theta)\hat a_\phi)$. Find the x-component of $\vec E$ at $P$. I found the vector in ...
0
votes
0answers
34 views

What coordinates does a line between two coordinates intersect?

I have a simple coordinate system like the following: In this example, I have a line between two coordinates $(2,7)$ and $(8,5)$. The line is drawn from and to the exact center of each coordinate. ...
0
votes
1answer
42 views

Find the vertices of the two right angled triangles each having area $18$ and such that the point $(2,4)$ lies on the hypotenuse and the other…

Find the vertices of the two right angled triangles each having area $18$ and such that the point $(2,4)$ lies on the hypotenuse and the other two sides are formed by the $x$ and $y$ axes. My work: ...
0
votes
3answers
24 views

A question on co-ordinates of intersecting lines…Given in picture below

Please do also MENTION how you got the solution.........
0
votes
1answer
21 views

Points defined by relations (an exercise from “System of Coordinates”)?

An exercise from "System of Coordinates" (by Gelfand, Glagoleva and Kirilov) asks me to "[t]ry to decide by yourself which sets of points are defined by these relations" and relations given are: a. ...
3
votes
0answers
67 views

Why does a figure look the same in every coordinate system?

After reading Maximilian M. Answer here: Gauss' Theorem - Can't understand a parameterization I'm trying to figure out why does a figure look the same in every coordinate system I choose. For ...
0
votes
1answer
36 views

Compare 2 coordinate systems in 3D space

How would i demonstrate that 2 coordinate systems are identical (that only a translation differentiate them) in 3D space? Let's say i have a coordinate system X Y Z and a coordinate system x y z.
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vote
0answers
111 views

Number of classes of K-sets

I am having a plane in N dimension. Th distance between 2 points (a1,a2,...,aN) and (b1,b2,...,bN) is max{|a1-b1|, |a2-b2|, ..., |aN-bN|}. I need to to know how many K-sets exist(here K-set refers to ...
5
votes
1answer
134 views

Coordinate Transformations

I am physics student. My mathematical background is quite weak. I just want to know the similarities (if there are any) between coordinate transformation of two kinds : Rotation of coordinate (and ...
0
votes
1answer
164 views

Unit Vector Based on Angle with XY-YZ-XZ Planes

this may be a simple one but lets assume I have 3 angles (a,b,c) and I want to know what unit vector makes such angles with the XY-YZ-XZ planes. Another question is that I wanna know if a,b and c are ...
1
vote
1answer
94 views

The Puzzle of Locating Points in a Quadrilaterally-Faced Hexahedral Creature

The Disclaimer This is NOT homework... I designed the story. I thought a name MIT would be funny, while something along the line of TULSA or SU will still be decent. I know the algorithm to Q3 and 3D ...
3
votes
1answer
160 views

Inverse of Ulam's spiral

I have a program and I need a function that takes a coordinate as input and returns an integer corresponding to the position in Ulam's spiral. The simple (but slow) way to do this would be to ...
0
votes
1answer
98 views

Converting from spherical coordinates to cartesian around arbitrary vector $N$

So if I'm given an arbitrary unit vector $N$ and another vector $V$ defined in spherical coordinates $\theta$ (polar angle between $N$ and $V$) and $\phi$ (azimuthal angle) and $r = 1$. How do I ...
1
vote
0answers
32 views

Geometric accuracy analysis of 2d rectangular models

I have reconstructed set of rectangular objects lie on a 2D plane (for ex. ABCD). All these objects are in a one coordinate system. On the other hand, I have reference models for all of them ...
1
vote
1answer
41 views

Transforming from cartesian to cylindrical

Here is the question: Transform $\textbf{A} = \hat{\mathbf{x}} 2 - \hat{\mathbf{y}}5 + \hat{\mathbf{z}}3$ into cylindrical coordinates at point ($x=-2, y=3, z=1$). What I have tried is this: ...
2
votes
1answer
78 views

Coordinate System Rotation and Cross Term

If I have a conic equation $$ 5x^2 - 4xy + 8y^2 = 36 $$ and $ \left[\begin{array}{cc} 5 & -2\\ -2 & 8 \end{array}\right] $ in matrix form, whose eigenvalues are 4 and 9, how would I rotate ...
1
vote
4answers
77 views

What is the basis of basis?

They say (here, for instance) that you can represent a vector, $\vec v$ as coordinate vector, $[v]_B$, in base, $B$, $$\vec v = v_1 \vec b_1 + v_2 \vec b_2 + \cdots = \begin{bmatrix}\vec b_1 & ...
0
votes
1answer
1k views

Finding the equation of a circle from given points on it and line on which the centre lies.

What are some effective ways to find the equation of a circle when you are given points lying on the circle and the equation for the line on which the centre of the circle lies. Here is an example of ...
3
votes
2answers
154 views

Check Points are line, triangle, circle or rectangle

How to determine geometric properties of four distinct points in a plane (x1,y1), (x2,y2), (x3,y3), (x4,y4) represented in the 2-D Cartesian coordinate system, whether these four points are on a ...
0
votes
3answers
62 views

What's the slope of the mirrored line?

If I have line $M$ with slope $m$, and line $A$ with slope $a$, and I wish to mirror $A$ over $M$ to form some new line $B$, what is the slope of $b$?
1
vote
1answer
17 views

How is the common syntax for a reference of points value?

I just wonder how do I reference a value of a point in a widely accepted syntax. For example there is the point $A(2\mid-6)$. How do I reference now the $x$-coordinate? I would go for $A_x$ and ...
1
vote
1answer
81 views

Re-Calculate Rectangle Width/Height After Translating One Coordinate

I'm trying to put resizing handles on the four corners of a rectangle, which can be dragged to resize the rectangle. What I'm having trouble with is calculating the new width, new height, and new ...
0
votes
2answers
40 views

How to work out the unknown vertex of a parallelogram given the other three

I have changed the numbers so you're not giving me the answers. Let A (1, 1), B (5,2), C (2, 4) and D (x, y) be the vertices of a parallelogram ABCD. What are the coordinates of vertex D? -As I am ...
0
votes
0answers
151 views

Convert from relative to absolute cartesian coordinate system

I am working on a building visualization application and a lot of elements here are defined using relative coordinate systems with given offset and basis. I.e. vectors defining $X, Y, Z$ axis, and a ...
1
vote
0answers
30 views

equation of a refracted straight line

we have got a line $$x-y=1$$ which after refracting from $x$-axis bends at angle $\pi/6$ from normal what's eqation of that line? what i did was that putting $y=0$ to get points on $x$-axis which ...
0
votes
1answer
32 views

Finding coordinates on line in 3d environment, given origin and direction

Working on a 3d game, I've encountered a math problem that gaming/stackoverflow hasn't been able to help with. Given an origin coordinate x,y,z, and a yaw/pitch direction away, how can I properly ...
2
votes
3answers
82 views

Simple way to parameterize two perpendicular vectors

Given are two vectors in $\mathbb{R}^3$, $\bar{u}$ and $\bar{v}$, such that they are perpendicular ($\bar{u}\cdot\bar{v}=0$) and of equal length ($|\bar{u}|=|\bar{v}|$). Is there a "nice" way to ...
0
votes
0answers
19 views

How to find new co-ordinates for points on a line dragged as a bezier curve.

I have a line with a set of points. I captured the start point and the end point of the line and found two control points for a bezier curve using the linear parametric equation. I construct the ...