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Questions tagged [coordinate-systems]

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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Indeterminate velocity components of a particle at the center of a polar coordinate system

Given coordinates of a particle and components of its velocity vector in Cartesian coordinates, I need to convert this data into polar coordinates. I had no problem to deduce the formulas which give $...
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1answer
33 views

Basis vectors in different coordinate systems

I was wondering about the following: The basis vectors used for the gradient, and curl in cylindrical and spherical coordinates are defined to be with unit vectors, why is that so? What if the basis ...
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Get coordinates of a specific point in 2D plane based on orientation vector

Coordinates : **$A(200,160), B(270,240), X??$ Point A can rotate in $[0,360)$ so it is the original of Unit circle and the orientation direction of point $B$ is in radian and here is equal to $\...
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1answer
74 views

Center of Gravity and Coordinate Systems

In below figure I need to find the coordinates of center of gravity which are $x$' and $y$' in order to find distances of $OG$ and $OS$. To explain the figure; $x^q+y^q<=1$, area of $ROP$ is ...
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1answer
21 views

Given $(x_1,y_1)$ and slope(angle), find $(x_2,y_2)$ coordinate

On a price/time chart where coordinates are defined in pixels, I am looking for formula to find $(x_2,y_2)$ coordinate. I already know the slope in degrees and $(x_1,y_1)$ coordinate. Help would be ...
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2answers
131 views

Probability that $\displaystyle \vert x\vert +\vert y\vert +\vert z\vert +\vert x+y+z\vert=\vert x+y\vert +\vert x+z\vert +\vert y+z\vert$

Real numbers $x, y$, and $z$ are chosen from the interval $[−1, 1]$ independently and uniformly at random. What is the probability that $$\vert x\vert +\vert y\vert +\vert z\vert +\vert x+y+z\vert=\...
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1answer
27 views

Find angle of line which runs perpendicular to a tangent trajectory of a point on 2d cartesian frame

As below, I am looking to find the variable '$\theta_e$'. Assuming the parameters which are given are the point ($x,y$) , ($L_h$),($d_e$), v, ($\theta_d$), ($x_d,y_d$). I do not have the parameter '$\...
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2answers
66 views

Where does this garbage line come from?

A question reads, "Find equation of the line which is equidistant from parallel lines $9x + 6y – 7 = 0$ and $3x + 2y + 6 = 0$." I solved it by doing the following:- Finding the distance between the ...
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1answer
27 views

(Co-ordinate Geometry) Vertices of a Triangle [closed]

The area of a triangle is $5$ square units. Two of its vertices are $(2,1)$ and $(3,-2)$. The third vertex lies on the plane $y-x+3=0$.Find the third vertex.
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get angles from vectors in 2D

A sensor $i$ with coordinates $(x_i,y_i)$ and its sensing angle $\varphi$ is given. A target with its coordinates $(x_k,y_k)$ and its face orientation (measured in radians) f_k is given. $d_{ij}$ is ...
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a conformal mapping using the tangent function?

I am dealing with a 2D coordinate transform, which is based on the tangent function, this way: x becomes p = tan(x) y becomes q = tan(y) the choice is due to tan() being able to "map" the finite ...
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how do I compute coordinates based on rotating object?

I cannot figure out how to calculate coordinates based on the degrees of rotation of another object. I hope this is right forum to ask this question. I am trying to write code for my game that will ...
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0answers
41 views

Question on Partial derivatives in inverse function changing from coordinate systems

I would like to ask a question about partial derivatives in the context of Rotations of coordinate systems. Say we have a coordinate system (unprimed) and its rotated version (primed). If the ...
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1answer
43 views

How to find a 2D coordinate field's corners in a 3D Coordinate field if I have 3x 3D points with 3x2D Points?

In order to solve "this" problem, i have to transform my corner-points from a 2D Space to my 3D Space. But my two coordinate fields are only defined by their relation to each other. They have the ...
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2answers
27 views

Do we use the x-axis for defining polar coordinates?

"To represent any point in a two dimensional space, you need two variables" right? For example (using our good old friend, The cartesian coordinates) we can talk about any point in two dimensional ...
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1answer
25 views

Given the coordiantes of the center and the radius of a circle, how can I determine if a point $(x,y)$ touches the circumference or not?

So let's say that I have a standard $(x, y)$ coordinates system, the center of a circle $(0,1)$ and the radius $(1)$. How can I determine that whether the point $(0,0)$ touches the circumference or ...
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Determining partial derivatives after coordinate transformation

I'm currently trying to figure out the partial deriviatives of a function, after there is a space transformation. $$ f(r_1, r_2, w) \rightarrow f(x, y, w)(2\sqrt{xy})^{-1} $$ Where $$ r_1 = x^2 \\ \\...
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2answers
32 views

Find the locus of midpoints dropped from hyperbola to asymptotes

If $PN$ is the perpendicular from a point on a rectangular hyperbola $x^2-y^2=a^2$ on any of its asymptotes, then find the locus of the midpoints of $PN.$ On drawing a rough sketch of the graph, I ...
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Calculate new X & Y coordinate based on compressed or enlarged rectangle

I have two Rectangles as Rect1 ___________ x'', y'' | |dy | | .x',y'| | | | | 0,0------------- Here the value of x''...
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Project position on Earth to higher altitude with local azimuth and elevation.

I have a position on Earth ($lat_1$,$lon_1$,$R_e$) of which I want to project a straight line with a known azimuth and elevation to a certain altitude, $r$. Thus obtaining new coordinates on the ...
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2answers
29 views

Stuck in something: How to write coordinates in one number?

I have a X, Y coordinate system which starts from 0 and ends in 255 on each axis. Thus, I can fit 65,025 numbers in it. Imagine each number as a pixel, so I have 65,0250 pixels in my coordinate system....
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2answers
37 views

Proof of orthogonality in a coordinate system [closed]

Given any coordinate transformation, how could I prove that the new coordinate system is orthogonal?
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1answer
49 views

Are the directrix line and focus unique for a conic?

How to prove of disprove the uniqueness of pair of (or single for parabola) directrix line and pair of focal points for a conics? (Ignore the degenerate cases and the circle.)
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2answers
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P and Q are 4 units apart and on the same side of variable straight line which touches a circle

My approach: I took a variable line ax+by+c=0 and took random points like (2,0) and (6,0). The I applied the formula for perpendicular distance and put it in the condition that PM+3QN=4. but this way ...
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3answers
35 views

Two functions f(x)=x^x and f(x)=x^(-x)

I was playing with desmos. Then I found a pair of interesting graphs, namely $f(x)=x^x$(the purple one) and $f(x)=x^{-x}$.(the green one) They both have their global maximum/minimum at a point about $...
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2answers
58 views

How to convert a 3D line into a 2D line?

I wanted to know if there is an algorithm I could use to show a 3D line on a 2D screen. The line is made up of 2 points with X, Y, Z coordinates. My end goal is to have a bunch of lines that may make ...
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1answer
29 views

Inverse of Roto-Translation Matrix

I'm trying to implement two JavaScript functions to calculate A 2D coordinate transformation from the reference frame $O$ to $O'$; The inverse transformation from $O'$ to $O$; The first step it's ...
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2answers
23 views

Does having two lines of symmetry $y=0$ and $y=-x$ imply that the shape also has lines of symmetry $x=0$ and $y=x$

I have been wondering if a shape/curve that has a line of symmetry along the lines $y=0$ and $y=-x$ is guaranteed to also have lines of symmetry along the lines $x=0$ and $y=x$. My gut feeling tells ...
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1answer
31 views

How to denote a set of all points that satisfy equation in Cartesian plane? [closed]

How can I denote a set of all points that satisfy $y=7-3x$ equation? Do you denote this set in set-builder? Thanks
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Finding and Comparing 2 Sensors Rotations, with same reference frame but different initial Orientation

Let's say we want to Compare two different Arm (Humerus) Rotations (series of quaternions) and we do not care about space translation but only for rotation. To measure each rotation we use the same ...
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Difference between coordinate map and standard coordinates?

I quote from W. Tu's introduction on manifolds: «On a manifold $M$ of dimension $n$, let $(U, \varphi )$ be a chart and $f$ a $C^\infty$ function. As a function into $\mathbb{R}^n$ , $\varphi$ has $n$...
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1answer
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four bar linkage coupled.

How can I get the point (x,y) at a four bar linkage coupled? The four bar linkage is free until is connected with another fifth bar, then it's not free anymore. See image below, when the bar FE is ...
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1answer
54 views

complex coordinate to screen coordinate problem

As an expansion to my fractal software, I've decided to add center plus width as an image location/definition. Which leads me to the question of how do I convert the complex number given to an x,y ...
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Finding a system of coordinates.

If $U=\{(x,y,z):x,y,z> 0\}$ and $u=x^2+y+z,v=x^2+y^2$ ($u$ and $v$ are functionally independent), how do I find a third function $w$ so that $(u,v,w)$ is a system of coordinates in $U$?
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1answer
31 views

How to calculate the co-ordinates of a quadrilateral knowing the side lengths

Hi I've come across a mathematical problem, which I can't seem to solve with my limited geometry and trigonometry knowledge. I need to draw a quadrilateral (may not be rectangle always). To draw this ...
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3answers
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In an acute triangle ABC, the base BC has the equation $4x – 3y + 3 = 0$. If the coordinates of the orthocentre (H) and circumcentre (P).

In an acute triangle ABC, the base BC has the equation $4x – 3y + 3 = 0$. If the coordinates of the orthocentre (H) and circumcentre (P) of the triangle are $(1, 2)$ and $(2, 3)$ respectively, then ...
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1answer
166 views

Prove that for every prime number $p$, there exist two pairs $(r,s)$ of positive integers for which $\frac1r-\frac1s={1\over p^2}$. [closed]

Prove that for every prime number $p$, there exist two pairs $(r,s)$ of positive integers for which $\frac1r-\frac1s={1\over p^2}$. How should I go about this proof?
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Question about analogies between vector calculus and matrix calculus

If working in $\mathbb{R}^N$ I have a set of $N$ functions $u_i = (x_1,x_2,...,x_N)$ such that the correspondence between $(x_1,x_2,...,x_N)$ and $(u_1,u_2,...,u_N)$ is unique, then I can build two ...
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81 views

Change of coordinates to solve an equation in partial derivatives

Given an equation in partial derivatives of the form $Af_x+Bf_y=\phi(x,y)$, for example $$f_x-f_y=(x+y)^2$$ How do I know which change of coordinates is appropiate to solve the equation? In this ...
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Find the locus of the middle point of the intercept on the line y=x+c made by the lines 2x+3y=5 & 2x+3y=8, c being a parameter?

Here's my shot: since the two lines are parallel, I figured that the middle point should be equidistant from the parallel lines,so using distance formula:- $ \frac{2x+3y-5}{\sqrt{13}}=\frac{2x+3y-8}{\...
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1answer
26 views

centroid algorithm robust to missing poins

I need to find a center point of a person given the coordinates of all the joints. The joints of a person can be represented as a nodes of a graph with a fixed structure. The catch is some of the ...
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1answer
48 views

What is a slope of a line?

What is a slope of a line? I understand that it is obtained by tan$\theta$ where $\theta$ is the inclination of the line but overall what does it means?
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1answer
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Is it that if we solve any first degree variable equations, we'll get a straight line on the coordinate plane?

If we solve any first degree variable equation will we always get a straight line on the coordinate plane? Is it because of this property we call these types of equations linear equations?
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Linear Equivalence of Algebraic Varieties

My question concerns the use of a linear change of coordinates applied to an algebraic variety. I would like to illustrate my question with an example: If we consider the curve $x^2+y^2-1=0$ over $\...
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What is the least eccentricity of an ellipse that can rest on a plane inclined at an angle $\alpha$ with the horizontal? [closed]

A perfectly rough plane is inclined at an angle $\alpha$ to the horizontal. What is the least eccentricity of an elliptic cylinder that resists rolling down the plane?
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1answer
42 views

Find a point that is perpendicular to line and write it in javascript [closed]

Hi and sorry if my post is not the best but is my first time in something like this I have seen this post, I have two directional points. Point A going to point B. Each point has an X and Y ...
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Get intersection point on 2d plane of two Beams by coordinates and rotation in degrees

I have 2 Beams on a 2d plane of wich i have the starting position and the rotation in degrees from 0-359°. I'm gonna use x and z for the coordinates, where 0° is +z, 90° is +x, 180° is -z and 270° is -...
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A book for questions on coordinate geometry

Can someone recommend me a book on coordinate geometry which focuses mainly on question solving and consists of ample amount of tough hybrid problems on 2 or more conics, topics like common tangents, ...
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Coordinate basis and coordinate systems

When we introduce coordinate systems, like spherical coordinates, one usually does it with respect to cartesian coordinates. What would be the right way to derive the (for example) spherical ...
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1answer
13 views

deducing an area of integration in cylindrical coordinates

If I am given an area characterised by $0 \leq z \leq 1-r^{2}$ from this how can I deduce the radius r and the angle with the x-axis, $\theta$ that will span the are and I can ten integrate over i.e. ...