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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Locus of a point $P$ inside $\triangle ABC$

$P$ is a point inside $\triangle ABC$. $X$, $Y$ and $Z$ are feet of perpendiculars from $P$ on $BC$, $CA$ and $AB$ respectively. Find the locus of $P$ is $XY=XZ$ and $A \equiv (4,3)$, $B \equiv ...
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1answer
27 views

How to evenly space a number of points in a rectangle?

Say I have a rectangle, with variable width and height, for example lets use: width = 20 height = 30 I would like to put n ...
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1answer
16 views

How to represent two coordinate system transformations as one

I'm working on a system of relative euclidean coordinate systems. I'd like to define every coordinate system relative to a global coordinate system, which I'll refer to as [0]. Then, for example, ...
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1answer
12 views

Phase of relative coordinate in the complex plane

If we have two points $z_1=x_1+iy_1$ and $z_2=x_2+iy_2$ in the complex plane and define the relative coordinate $z=z_2-z_1$, we have that the length of $z$ is the Euclidian distance between the ...
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1answer
31 views

Voltage Distribution Inside a Cylinder [on hold]

I was assigned this problem, and quite honestly I do not know where to begin. If I could get some help and an explanation of the Bessel function, also? Thank you. I know my conditions are: ...
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triple integral reduction

I have a triple integral of this kind $$\int_0^t{dx f(x)\int_{t-x}^{\infty}{dy g(y)\int_{t-x-y}^{t+\Delta t-x-y}{dz\delta(z)h(x,y,z)}}}$$ where $\delta$ is the Dirac Delta function and the other ...
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2answers
30 views

Calculating the lengh of $AG$ in a square

$ABCD$ is a rectangle and the lines ending at $E$, $F$ and $G$ are all parallel to $AB$ as shown. If $AD = 12$, then calculate the length of $AG$. Ok, I started by setting up a system of axes where ...
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1answer
34 views

Shortest path between two points that touches a line [closed]

A man starts from from the point $P(-3,4)$ and will reach the point $Q(0,1)$ touching the line $2x+y=7$ at $R$. What are the coordinates of $R$ on the line if it is chosen so that he will travel in ...
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1answer
12 views

Dealing with negative areas— coordinate geometry

Question: Find the area of a quadrilateral in the Cartesian plane, whose vertices are (-4, 5), (0, 7), (5, -5) and (-4, -2) My solution: [I meant to draw ...
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1answer
13 views

determine transform matrix given two points

You'll have to excuse me if this is a dumb question, but I am only familiar with the basics of linear algebra. I have the coordinates of the SAME point in two different coordinate systems. Is it ...
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8 views

Confusion about coordinate transforms

Lets say I have a camera aligned with the world coordinates system. I rotate it by 180 degrees around the z axis and then by 20 degrees around its new y axis. I have been reading about Euler angles ...
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1answer
13 views

Inverse rotation euler angles

I have three angles representing a rotation (Pitch, roll and yaw). I need the inverse rotation (working on coordinate system transforms). What I do now is transforming these angle to a rotation matrix ...
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2answers
72 views
+50

Find the locus of points M the difference of the squares of whose distances from two given points A and B is equal to a given value c.

Find the locus of points M the difference of the squares of whose distances from two given points A and B is equal to a given value c. For what values of c does the problem have a solution? I am ...
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0answers
11 views

Pairing Two Point Clouds

So I have two point clouds $X$ and $Y$ each with $N$ points in the familiar $\mathbb{R}^3$ euclidian 3D space. I then have an inter-point distance $d(\vec x_i,\vec y_j)$ which is zero if $\vec x_i$ is ...
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2answers
13 views

Coordinate/matrix multiplication

If I multiply a 3d coordinate (padded with a 1 to make it a 4x1 matrix) with a transformation matrix, I get a 1x4 matrix which contains my new (transformed) 3d coordinate. Knowing that matrices must ...
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3answers
61 views

Trying to understand polar coordinate vectors

I'm trying to understand what the unit polar coordinate vectors (I'll denote them $\hat r$ and $\hat \phi$) are and if they form a basis for $\Bbb R^2$. So from what I understand, $\hat r$ points ...
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1answer
30 views

Formula for the angle of a line $y = mx$ as a function of $m$.

I was wondering if there was a way to calculate the angle made by a line $(\space y=mx)$ in the Cartesian plane using only $m$. I used the Pythagorean theorem in this figure: $$AO= ...
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1answer
25 views

Collision Detection in Finite but Limitless Space

Doing collision detection on two arbitrary rectangles is easy, given their coordinates and dimensions. In regular 2d-space, that is. But what about "finite but limitless" space, say a screen area ...
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1answer
20 views

Spherical coordinates on cartesian straight lines

I'm trying to solve this problem: Compute the volume of the solid bounded by: the surface $(z+1)^2=x^2+y^2,$ the surface $4z=x^2+y^2,$ above the $xy$ plane. I want to do it with spherical ...
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2answers
41 views

Understanding Spherical coordinates on ellipses.

I was given the following problem: $$\iiint\limits_D (4x^2+9y^2+36z^2)\,dV,$$ where $V$ is the interior of the ellipsoid $$\frac{x^2}{9}+\frac{y^2}{4}+z^2=1.$$ The problem gives what the new ...
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Trying to convert $\theta$ and $\phi$ to relative to point of view on surface of sphere.

I'm not sure if the title is very descriptive of what I'm trying to do. Let's say I have a sphere with radius $r$ and let's say I'm standing on the surface of that sphere (this is actually Earth but ...
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2answers
125 views

Cylindrical coordinates on elliptic paraboloids.

I want to compute the volume bounded by: the cylinder $x^2+4y^2=4$. the $z=0$ plane. the elliptic paraboloid $z = x^2 + 6y^2$. I would like to use cylindrical coordinates. However I have never ...
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1answer
14 views

Co-ordinate vector of the linear transformation of x

$T$ is the linear transformation of $V$ ($n$-dimensional) to $W$ ($m$-dimensional) and {$b_1,...b_n$} is the basis $B$ for $V.$ Given any x in $V$, the coordinate vector $[x]_B$ is in $R^n$ and the ...
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4answers
80 views

How to find coordinates of reflected point?

How can I find the coordinates of a point reflected over a line that may not necessarily be any of the axis? Example Question: If P is a reflection (image) of point (3, -3) in the line $2y = ...
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3answers
41 views

$x^2+y^2=5$ and point $(-4,3)$. Find the equations of the tangents to the circle and the point.

$x^2+y^2=5^2$ and point $(-4,3)$. Find the equations of the tangents to the circle and the point. This question came up in class and we were unsure of how to do it. Our class spent a good 20 minutes ...
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0answers
26 views

Co-ordinate chart and components of a vector field.

Q) Using a coordinate chart, give a formula for the components of the vector field $[v,w]$ in terms of the components of $v$ and $w$. Where $[v,w]: f \mapsto v(wf) - w(vf)$ I don't know what the ...
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0answers
39 views

Determine third point of triangle when two points and all sides are known

I am solving basically the same problem as asked in this thread Determine third point of triangle when two points and all sides are known? I know 3 sides of a triangle and positions of two of them. ...
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1answer
12 views

Number of straight line through point forming same area with axes

I am given a point $P(2,3)$ thru which passing line forms triangle with axes of area $12$ , so how many lines will pass thru $P$ making same area with axes? Writing intercept form of line ...
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8 views

Rotate a point on circle by an angle such that the point attains a new coordinate axis.

I have this circle with known radius and centre w.r.t to both new and old coordinate axes given by NBase and Base respectively. I need to find a point P and Theta such that when vector OP is rotated ...
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1answer
14 views

Linear mapping coordinate question - need help

I am given the set $B=[(2,3),(1,2)]$ and $C=[(2,1),(1,1)]$. $L: \mathbb R^2\to \mathbb R^2$ is the linear mapping such that $[x]_B = [L(x)]_C$ (like coordinate vector stuff). I am told to find ...
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3answers
50 views

why $x^3\space +\space ax^2\space -x\space -2$ can only have one solution greater than zero

what is the proof for the above equation always having exactly one solution greater than zero for all values of a I cannot see how to prove this because you cannot factorise the polynomial and I am ...
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1answer
11 views

Find the coordinate of the point at which each straight line crosses the co-ordinate axes?

Find the coordinate of the point at which each straight line crosses the co-ordinate axes? 5x-3y = 10 is (0,10/3) the answer?
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1answer
41 views

Finding coordinates with respect to a basis

Let $B={{(1,x,x^2)}}$ and $C=(1,3x+4x^2,2x+3x^2)$ be bases for $P_2(\mathbb R)$. Find the coordinates of $x$ and $x^2$ with respect to the basis $C$. I'm a little stuck on where do begin for this ...
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1answer
15 views

equation of y=f(x) after it has been reflected in the line x=k

What is the equation of y=f(x) after it has been reflected in the line x=k For example if k=0 then it would be the y axis so the new equation would be y=f(-x) In addition what is the equation of ...
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1answer
30 views

How can I get a smooth distortion on a circle with a function g(x,y)

Let's say, $$f(x,y)=x^2+y^2=1$$ gives the unit circle. Now I would like to get a smooth distortion on the circle with a function $g(x,y)$. my guess is to consider the perimeter as one dimension, so ...
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1answer
33 views

Barycentric Coordinates of the circumcenter of an arbitrary triangle

Given points $A(1, 0, 0), B(0, 1, 0), C(0, 0, 1)$ in barycentric coordinates, and points $P(x_P, y_P, z_P), Q(x_Q, y_Q, z_Q), R(x_R, y_R, z_R)$, what would the barycentric coordinates of the ...
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14 views

Convert geodetic coordinates to cartesian coordinates

I am working on some simulation software that will represent a number of entities in a defined geographic area in the world. The part of the software that I am currently working on is to implement ...
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1answer
24 views

Is it possible to write all of the functions in terms of polar form?

Is it possible to write all functions in terms of polar form? For example, the equation of the circle with radius one can be written like $r=1$ I'm wondering whether reform the equations of all curves ...
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1answer
22 views

Transformation to elliptical coordinates

I'm currently struggling to make any progress with this question. I'm a little bit thrown by the inclusion of cosh and sinh. I am aware of all of the definitions, just need guidance with approach.
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26 views

Finding a way between two points

Let's assume we have two points $A(x_1,y_1)$ and $B(x_2,y_2)$ in 2-D space. And we need to find a trajectory for going from one point to the other. But the problem is that in this space prohibiting ...
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54 views

Polar coordinate system of DE's to be written in cartesian form.

Suppose we have a system in polar coordinates: $\dot r = -r$ and $\dot \theta = \frac{1}{\ln{r}}$, we are asked to solve for $r(t)$ and $\theta(t)$ explicitly, so I just integrated both equations so ...
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19 views

Jacobian equals the product of scale factors

I have to prove that in 2 dimensions $J(\frac{x,y}{q_1,q_2})=h_1 h_2$ (1), where $q_1, q_2$ are the new mutually perpendicular coordinates and $h_1, h_2$ are the respective scale factors (exercise ...
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1answer
16 views

How is a coordinate system called where values increase to the bottom instead to the top?

In some computer graphics libraries the coordinate system is almost like the "usual" cartesian coordinate system. The only difference is that the $y$ values increas to the bottom, not to the top. ...
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1answer
23 views

Transformations from n-sphere coordinates to cartesian coordinates.

I was wondering how one would proceed to convert between coordinate systems in $ \mathbb R^n $. For $ \mathbb R^2 $ the conversion is easy and just basic trigonometry. Given $(r, \theta)$ we can ...
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1answer
33 views

Calculate X Y Z from two specific degrees on a sphere

I am a programmer, don't know much about advanced math. I would need the exact formula(s) that could achieve this, so I can translate it to my programming language. I am having a headache trying to ...
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27 views

How to check if a set of coordinates creates a polygon?

Well, hello. I've got a set of coordinates and i want to check if it creates one polygon or 2 (or more) polygons. Coordinates are being read from input stream, one after another, for example: ...
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2answers
17 views

Finding the co-ordinate vector

I can find the co-ordinate vectors for all $x$ in $R^n$ but I can't wrap my head around the ones for $x$ in $P_n$. Here is a question: Let $V$ be the space $P_3$ of all polynomials of degree at ...
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1answer
18 views

Coordinates of a vector under a basis in a Hilbert space?

Given an arbitrary basis $\{m_1, \dots, m_n \}$of a Hilbert space $H$ (or just think it as $\mathbb R^n$, and I think the methods should be the same) with given inner product, how can we find the ...
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1answer
27 views

How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$

Problem : How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$ My working on this : Two lines are perpendicular if the sum of ...
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2answers
31 views

Find the co-ordinates of the point of intersection

I have the function $$y=2x^2-3x$$ How do I find the co-ordinates of the point of intersection of the lines tangent to the curve at $y=-1$? One point where $y = -1$ is when $x = \dfrac 12$. I took ...