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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1answer
13 views

Orthocentr and circumcentre formula in 3D

Given three points in a 3D coordinate system, how can we find the orthocentre and circumcentre of the triangle formed by these points?
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2answers
34 views

How to prove that this coordinate system is ortoghonal?

I have a coordinate system $(u,v)$ given by: $$ \begin{eqnarray} u&=&xy \\ v&=&\ln(y) \end{eqnarray} $$ How can i check if it is ortoghonal, find the unit vectors and find the ...
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0answers
17 views

Find the equation of the conjugate of the hyperbola $xy+4-4x-2y=0$

Problem : Find the equation of the conjugate of the hyperbola $xy+4-4x-2y=0$ My approach : Solution : After simplifying the given equation of the hyperbola $(y-4)(x-2)=4$ $\Rightarrow $ ...
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5answers
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Can area be irrational?

I'm stuck in a question of my book which says: If in an equilateral triangle the coordinates of two vertices are integral then what can we say about the coordinates of the third? The answer is that ...
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3answers
183 views

Find X location using 3 known (X,Y) location using trilateration

I post this question in stackoverflow here and was advised it was best suited for here. I am trying to understand the maths behind trilateration, we have 3 access points (AP 1,2,3) and we know the ...
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1answer
18 views

Calculating the length of $DP$ in a rectangle.

$P$ is a point in rectangle $ABCD$. Calculate the length of $DP$ if $AP = 3$, $PC = 5$ and $BP = 4$. How do I go about by doing this? I clearly can't use Pythagoras because the hypotenuse is not a ...
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1answer
29 views

Distance Between Pair Of Parallel Straight Lines

If the equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel straight lines then the distance between them is?
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3answers
33 views

What will be the other vertex of the triangle?

Two vertices of a triangles are $(5,-1)$ and $(-2,3)$. If the orthocenter of the triangle is the origin, what is the other vertex ? My approach was that since the three vertices and the orthocenter ...
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1answer
73 views

Manifolds, coordinate systems, books

Which books, say Lee's Introduction to Smooth Manifolds or Munkres' Analysis on Manifolds explains how the theory of a differentiable manifolds can be used to solve a problem that is expressed in a ...
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0answers
13 views

Specify coordinate system from normal, azimuth and elevation angles.

I have a finite plane in $\mathbb R^3$, with a normal unit vector $$\vec n=<n_x,n_y,n_z>$$ at the center of this plane $C_1(x_1,y_1,z_1)$. The direction of the normal unit vector $\vec n$ is ...
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1answer
20 views

Line plane intersection

I have two planes in $\mathbb R^3$ as shown below: axes representation corrected after MvG's comment Each plane is a finite area, a rectangle with length and width $H_l, H_w$. Each plane has its ...
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3answers
38 views

Three dimensional rotation of equations.

I have a set of equations that describe a wire in (100) direction. I want to rotate the wire such that it's in the direction (111). My initial plan (which failed) was to use Euler coordinates and ...
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1answer
758 views

Rotating a point in spherical coordinates around Cartesian axis

If I have a point in spherical coordinates, and I rotate it around one of the Cartesian axes, what will be the new spherical coordinates for the point? Both spherical and Cartesian coordinate systems ...
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2answers
22 views

find the equation of a sphere with endpoints A and B where B is the point of tangency of the sphere and the plane

Find the equation of a sphere with a diameter that has endpoints $A(1, 8, −2)$ and $B$, where $B$ is the point of tangency of the sphere with the plane $−9x +6y + 2z = 2$. Now i know that i can get ...
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2answers
319 views

Find parametric expression of an arc given its start point, end point and central angle in 3D cartesian coordinate system

In a 3D cartesian coordinate system, the coordinates of start point and end point have been given as $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. If the central angle of the two points (the one smaller ...
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0answers
20 views

Pair Of Straight Lines-Bisector Based Problem

If one of the lines of the pair ax^2+2hxy+by^2=0 bisects the angle between positive direction of the axes a,b,h, find the ...
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1answer
14 views

How to check whether two unit vectors are parallel?

Lets say we have the vectors, $3\hat i+3\hat{j}$ and $5\hat i+5\hat j$. Are these vectors parallel? Is this process is similar to the equations of lines? $3x+3y-9=0$ etc. So if I have a vector ...
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0answers
17 views

Do affine spaces have coordinate transformations?

I asked a question on Physics SE and there seemed to be some confusion as to whether affine spaces could have coordinate transformations. Specifically, the particular space I was working with was ...
1
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1answer
30 views

How do you convert velocity given a heading and speed to ECEF coordinates?

If you are given positional data in latitude, longitude, altitude along with a given velocity and heading, how do you convert the velocity into Earth Centered Earth Fixed (ECEF) based values? In this ...
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1answer
25 views

Pair Of Straight Lines Perpendicularity

Find the condition that one of the lines given by $ax^2+2hxy+by^2=0$ may be perpendicular to one of the lines given by $Ax^2+2Hxy+By^2=0$. I tried out like $m_1 + m_2 = -2h/b$ and $m_1\cdot m_2=a/b$ ...
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1answer
11 views

A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate…

Problem : A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes on points P and Q . As L varies find the absolute minimum value of OP + OQ ( O ...
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0answers
14 views

How to determine the precision of converted coordinates

I wrote an app that I use that converts latitude and longitude coordinates between the different forms that I encounter. After reading a question on Geographic Information Systems SE I realized I ...
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0answers
23 views

Check if a point is inside a rotated 2D NACA 0012 airfoil

I've already checked the rotated rectangle problem but this is (I think!) a little more complicated. I have a CFD calculation of a 2D NACA 0012 airfoil and I need to test if a point is inside the ...
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0answers
7 views

Chloropleth based on Scalable Coordinate System

In excel: I have a list of lat long coordinates within a city. My aim will be to create a chloropleth grid on a map in which, the number of the coordinates, the weighting of those coordinates or ...
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1answer
22 views

Equation of one of the two lines whose angle bisector is given.

A ray of light falling along the line $ lx+my+n=0 $ strikes a plane mirror at point $P$. Find the equation of reflected ray if $px+qy+r=0$ is the equation of normal to the plane at point $P$.
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15 views

Change of coordinate matrix for polynomials

So I am trying to do a simple change of basis. I have my 2 basis for $p_1$: $\beta={(1,x)}, \beta'=(1+x,1-x)$ The matrix for coordinate change from $\beta$ to $\beta'$ is $$Q = \begin{bmatrix} ...
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2answers
115 views

Scalar product invariance

The question is somehow silly, but I can't seem to find a way out right now. Consider the vector $v\in\mathbb R^2$, expressed in Cartesian coordinates as $(1,1)$ and in polar coordinates as $(\sqrt ...
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1answer
59 views

A point $P$ is selected inside an equilateral triangle. If sum of lengths of perpendicular dropped on to sides from $P$

Problem : A point $P$ is selected inside an equilateral triangle. If sum of lengths of perpendicular dropped on to sides from $P$ is $2014$, then $\frac{\mathrm{length\; of \; altitude \; of \; ...
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0answers
26 views

Spherical coordinates what are the coordinates of a vector?

I am getting a bit confused about the language for coordinate systems. I have chosen spherical coordinates as an example, but my confusion is general. Let's say we have a vector $$\vec A=A_r ...
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2answers
26 views

How to know if two points are diagonally aligned?

If I have two points at different X/Y coordinates, I know that: They are vertically aligned if both are at the same X coordinate; They are horizontally aligned if both are at the same Y coordinate. ...
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2answers
822 views

How to calculate the coordinates of orthocentre.!!

How to calculate the coordinates of orthocentre.!! I was surfing through the net and got this formula.. $$x-\rm coordinate= \frac{x_1\tan A+x_2\tan B+x_3\tan C}{\tan A+\tan B+\tan C}$$ ...
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0answers
31 views

Mapping cartesian coordinates to circular coordinates

I have some "rectangular" x,y coordinates which I like to convert to "circular" coordinates. Notice I'm not sure if I'm using the correct terms here, so bear with me - I drew an example to show how ...
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1answer
570 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 ...
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0answers
12 views

Parabolic Coordinates and the Normal Derivative

I would like some help with the following problem. Thanks for any help in advance. Determine the largest region Ω’ in R^2 spanned by (u,v) such that the transformation T that defines parabolic ...
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0answers
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Mapping A point from one 3D Coordinate System to Another 3D coordinate System with Euler Angles between the two systems given

Suppose I have a point in the green coordinate system, and I wish to describe it in reference to the orange coordinate system. I know the roll, pitch, and yaw of the green system with respect to the ...
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1answer
25 views

coordinates of 3rd point (vertex) of a right triangle knowing lengths and direction

In a last post I wanted to know the 3rd point of vertex, actually I have some similar problem .... I think I have all data.. for example...: 3 vertex cordinates in order to have the direction(gray ...
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1answer
11 views

Coordinate transformation (or conversion) into yards

Following is a soccer field with its dimensions. There is a similar field, but I am capturing coordinates via mouse-movement. So, what (115,75) shows here, is ...
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0answers
27 views

distance in n-dimensional space

According to answer of this question : Distance between 2 points in 3D space (in spherical polar coordinates) The distance between 2 points in 3 dimensional space is : $$ ...
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1answer
21 views

Square labeled with same number.

Recently I met this combinatorics problem: "Let all points with integer coordinates in a plane be labeled with one of the numbers $1,2,3,...,n$. Prove that there is a rectangle whose vertices are ...
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1answer
24 views

How to rotate an orientation (Euler angles)

If I have an orientation defined by Euler angles and I want to simulate a rotation of the coordinate system about the origin (doesn't matter to me how the rotation is specified), how would I get the ...
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0answers
20 views

How to express standard deviations and correlations of 6 points as one measure of uncertainty?

Algorithm that I use, uses a weight matrix P of size n x n to compute $XPY^T$ where $X$ and $Y$ are 3 x n matrices - representing X,Y,Z coordinates for n points. This means that points are weighted ...
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0answers
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Making Homogenous Parabola Equation

Find the locus of the mid-points of the chords of the parabola $y^2=4ax$ which subtend a right angle at the vertex of the parabola. Now we say $y^2=\frac{4ax(yk-2ax)}{k^2-2ah}$ coefficient of ...
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1answer
26 views

How to get coordinates of a point after an image is rotated? (with images)

I have a problem that involves a rotating image and finding a previously known point. Firstly, there is a sequence with the rotation. We start with an empty image. A line is drawn vertically, ...
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0answers
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linear functional basis and affine map

Suppose that the domain under consideration is the right triangle with coordinates (0,0), (1,0), and (0,1). At each vertex, let $\sigma_k(x,y)$ be such that $\sigma_k(x_k,y_k) = 1$ and ...
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1answer
296 views

Triangle and parametric coordinates

I'm studying on a book where it says: "A triangle is the set of points where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates ...
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1answer
67 views

Need Help in Coordinate Geometry (Straight Lines) [closed]

A line $L$  is drawn from the point $P\equiv(4,3)$  to meet the parallel lines $L_1: 3x + 4y + 15 =0$  and $L_2 = 3x + 4y + 5 =0$ at points $A$  and $B$ respectively. From $A$, a line perpendicular ...
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1answer
14 views

How do I find the symmetrical point B given the centre of symmetry C and another point A?

I have a point $A (-2k; 3)$ and a point $B$ that is symmetrical to the point A given the centre of symmetry $C (-1; 0)$. I tried applying the following formula, where $x_o$ and $y_0$ are the ...
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2answers
34 views

Calculate new(x,y) for a line

Suppose if tanks has to rotate its main gun by $30^\circ$ to hit the target, what will be its new $(x,y)$ coordinate or a formula to calculate it as shown in image? If bullet is fired from the main ...
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3answers
52 views

The geometric meaning of certain mappings written in cylindrical or spherical coordinates

What is the geometric meaning of the following mappings, that are written in cylindrical coordinates? The mappings are: $$(r, \theta, z) \rightarrow(r, \theta , -z) \\ (r, \theta , z) \rightarrow (r, ...
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0answers
27 views

Cylindrical coordinates - Orthonormal system

Using cylindrical coordinates and the orthonormal system of vectors $\overrightarrow{e}_r, \overrightarrow{e}_{\theta}, \overrightarrow{e}_z$ describe each of the $\overrightarrow{e}_r$, ...