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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How to calculate angles and areas (circles)- AS Maths

Hi here's the question: A(-1,-4) and B(6,-5) are points on the circumference of a circle, centre D(3,-1). The tangents at A and B intersect at C. How would I find the angle ACB and the area of ACBD? ...
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Using azimuthal and polar angles in ECEF coordinate system

I have a physical cone, which its vertex located in some point (x,y,z) in ECEF coordinates, and I want to check if another point is inside this cone. In order to do it, I have to take into ...
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1answer
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Benefit from local coordinates

I am reading Elliptic Curves by Anthony Knapp. Its the first time that I am dealing with local coordinates. In page 21 he introduces them as follows: Let $[x_0,y_0,w_0]\in \mathbb P_2(k)$ where $k$ ...
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1answer
23 views

Clamp Distance Between Two Vectors

I was wondering if there is a formula to clamp distance between two Vectors. Let me elaborate. I have two Vectors, say, $V_1(x_1,y_1)$ and $V_2(x_2,y_2)$. I can find the distance '$d$' between them ...
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1answer
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convert coordinates from non-orthogonal axes to cartesian in 3-dimensions

I'm having issues converting from a non-orthogonal coordinate space (abc) to a cartesian space (xyz). I think I may have just thought myself into a corner, and I can't get out. The systems have a ...
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3answers
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Find coordinates of the rotation center

My software is going to control a Laser. I know the Laser's current Position defined as $P_1$ with coordinates $(x,y)$ and the place where it will be after a clockwise rotation around a point $C$, ...
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1answer
14 views

Calculate x and y coordinates of n'th cell in table

If we have table with $c$ number of columns and $r$ number of rows, and we iterate through the table from left to right and then to the next row (below), how do we calculate to which row and to which ...
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2answers
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Transform of the Cartesian plane that maps hyperbolic arcs $xy = C$ to line segments

I have the finite set of curves: $$y = \frac{C}{x}, \qquad C = 2, 3, \ldots, C_{\max},$$ with $C$ and $x$ positive integers, $2 \le x \le C$ ($x$ varies on a finite domain). Is it possible to apply ...
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1answer
27 views

Calculate mean and std.dev from a lot of coordinates

How do i calculate the mean coordinate and the standard deviation of a cloud of (x,y) coordinates. I know how to calculate the mean, but i am struggling with calculating the std. deviation.
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Locus of point moving under constraints [closed]

OA is a fixed line segment of length a. Let OABC be a quadrilateral so that AB=b, BC=c, & CO= d. Find the locus of B. < Four bar chain mechanism>
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1answer
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Given 4 coordinates from the perimiter of a square, can the square be constructed?

I have a square, tilted at an unknown angle. I am given 4 coordinates of the square. They lie on the perimeter, one per side. With these 4, and nothing else, am I able to determine the vertices of ...
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Coordinate Geometry Help (circles + trigonometry) [on hold]

Question : Find all points $(x, y)$ {if there are too many then number of points is enough} which lie on or inside the circle $x^2 + y ^2 = 9$ and satisfying the equation $\tan^4 (x) + \cot^4 (x) + 2 ...
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Conditions for point lying inside triangle formed by three complex numbers.

The question states $z_1,z_2,z_3$ are three non-collinear complex numbers such that $$z=\frac{lz_1+mz_2+nz_3}{l+m+n}$$ lies inside the triangle formed by $z_1,z_2,z_3$. If $l,m,n$ are the ...
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2answers
55 views

How can I calculate Distance of line?

I have a picture. I want to measure of $P_{1}$ to $P_{4}$ distance. Also I know $P_{1}$ to $P_{2}$ to real distance. and $P_{2}$ to $P_{3}$ real distance $P_{1}-P_{2}$ real distance = $100$ mm ( ...
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1answer
32 views

Calculating the x, y coordinate a set distance between two points

I'm trying to calculate the x and y coordinates that are a set distance between the coordinates of two pixels in an image. For example, if I travel from my original location (x1=4, y1=3) to a new ...
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How to obtain a rectangle's side's positions if its origin isn't in its middle? [closed]

Basically I have an algorithm which generates rooms and corridors randomly and each time a room is made, a new corridor is placed on $1/4$ of the room's sides and its origin point is set to that ...
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1answer
64 views

Area of triangle formed by angle bisector, altitude and median

Question:- Given a triangle ABC with side length a, b and c. Calculate the area of a triangle in terms of a, b and c formed by angle bisector from vertex A, altitude from vertex B and median from ...
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1answer
9 views

How to derive $r, \theta, \phi$ for the sperical coordinate gradient?

I'm trying to figure out how to get the gradient in spherical coordinates. I'm as far as the author writes in this answer: http://physics.stackexchange.com/a/78514 and I understand how and why to get ...
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1answer
29 views

coordinate geometry : intersection of a curve with a line

I'm having difficulties with the question below. It is from a Cambridge past paper. The equation of a curve is $xy=12$ and the equation of a line $l$ is $2x+y=k$, where $k$ is a constant. In the ...
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1answer
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Finding coordinates of the third point of a triangle from given?

In ABC triangle we know the coordinates of A and B vertices. We also know lengths of 2 edges shown in the picture and the third edge is calculatable. What is the most efficient functon to find x3 and ...
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1answer
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Short question about spherical coordinates

If I have a vector orthogonal to the $x$-$y$ plane of an $xyz$ axis system, I mean, a vector with just $z$ component: How can I express it in spherical coordinates?
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Combining two different 2D coordinate points in order to find a 3rd dimension

I'm working in a project where I'm working with two cameras that give me the coordinates of a determined object. The coordinate systems of the two cameras are separated by a known distance (let's ...
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1answer
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How to get a Right Triangle's points' coordination in the space?

I have a Right Triangle with equal legs of 1 unit long rotated on 3 individual angles in the space like in the picture below: As could be seen in the picture, the input I have are the angles 'a' ...
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1answer
39 views

How to calculate Cartesian coordinates for an element after rotation has been applied?

I have a square on a Cartesian coordinate system with origin (0,0) on top left (yellow arrow from the picture). The initial coordinate of the square from the ...
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Coordinate - Resizing and Positioning

I have an image that is 1000x134 referred to as logo I have another view in the back The user is allowed to pan, pinch, and rotate the logo to position it where ever they want on top of the ...
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Show if a point belongs to the area of a complex polygon

I would like to know if there is a way to know if a point belongs to the area of any polygon just by knowing the coordiantes of all the points making the boundary of the polygon , given thaht where I ...
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How can I transform coordinate systems based on quaternion data?

I have a single rigid body object, and its orientations in quaternion with respect to two coordinate systems, each is called original and prime, respectively; therefore, I have two quaternions ...
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Missing equation in coordinate system transformation?

I want to transform a differential equation from polar coordinates $(r,\theta)$ to the following $(u, v, \phi)$ coordinate system: $$ u = r \cos(\theta - \phi) \\ v = r \sin(\theta - \phi) \\ \phi = ...
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1answer
26 views

Point where two hyperbolas touch each other

This is a simple question that showed up in my research, but it has been vexing me a fair bit. Consider the unit square $\{(x,y): 0\leq x,y\leq 1\}$ and define two hyperbolas restricted to the unit ...
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1answer
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x1, y1 and radius are given - can anything be assumed about x2, y2?

I have a list of lat/lng coordinates. Given the coordinates x1, y1, and a radius r -- is there anything I can assume about the coordinates that fall within the radius of x1, y1? For example, can I ...
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2answers
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Constant Moving Speed

I've made this graph: https://www.desmos.com/calculator/czk3ylyokj As you can see, the purple point is slowing down as it approaces the extreme point. How can I make this point move with constant ...
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1answer
17 views

Finding the formula of a line when given a line and angle.

Assume I have a line $y_1 = m_1x + b_1$. And I'm given $\theta$ degrees. How do I find a line $\theta$ degrees counterclockwise from the line.
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How to convert coordinates in a left-handed graph to a right-handed graph

I have the following coordinates which describe points on a left-handed graph and I need to convert the graph to be right-handed instead: $(0,0), (21,56), (38,0), (51, 35), (-5, 38)$ Is it as ...
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Gradient in local coordinates on a manifold with Riemannian metric

Let $M$ be a smooth manifold with a Riemannian metric g : $TM\otimes TM$ -> R If f is a smooth function from M to R, the gradient of f with respect to g is the vector field $\nabla f$ defined by ...
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One form and Vector fields on a manifold in terms of local coordinates.

Prove : $d$$\omega$$(V,W)$=$V \omega (W) - W \omega(V) -\omega([V,W])$ in local coordinates where $\omega$ is a one-form and V,W are vector fields on a smooth manifold M. I do not know how to ...
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Normal to the x-direction

Homework question says "If both surfaces normal to the x-direction are then insulated so that they are impervious to heat flow." In two dimensions, (x,y), two surfaces normal to the x-direction ...
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1answer
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Find point inside circle but outside of n- other circles

There is one green circle and 0 to n red circle(s). I'm trying to find a point inside the green circle, but outside all red ...
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1answer
24 views

Spherical Coordinates ( plane y = -x)

I am attempting to express the plane y = -x in spherical coordinates. Is there any clean way to do this? I have expressions for rho, theta, and phi in my text book but I don't think anyone of those ...
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2answers
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Locus of image of point in a line.

I am given the following question: Find the locus of the image of the point $(2,3)$ in the line $$\text{L}:(2x-3y+4)+k(x-2y+3)=0$$ where $k$ is any real number. Attempt at solution. I ...
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1answer
19 views

Coordinate-geometry curiosity question

How can we draw a triangle give one of its vertex and the orthocentre and circumcentre? I tried to invoke the concept of 9 point circle and tried using the centroid but could not succeed in making ...
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1answer
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Analytic-geometry rotation concept

I am confused how my book comes up with the following formula- Lets consider a Right angled Isoceles triangle with $2$ vertices on hypotenuse given as $(x_1,y_1)$ and $(x_2,y_2)$ Now the 3rd ...
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1answer
27 views

Converting between unit vectors

Sorry for really simple question but I was wondering, if I want to swap between a vector in the polar coordinates, and get to Cartesian coordinates, how do we determine where the radial and angular ...
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1answer
24 views

Coordinates of a point at a given distance from (x,y)

I seem to have forgotten my coordinate geometry and this is absolutely blank. Say I have $(x_1,y_1)$ and a distance $d$. Is it possible for me to solve for what the point $(x_2,y_2)$ is? To explain ...
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Distance and Coordinates in fractional dimensions and the creation of functions with non-integral numbers of paramters.

Background: The Euclidean distance between two points in $n$ dimensions, where $n$ is a positive integer, and position can be described by a vector is given by... $$D_E=\left(\sum_{k=1}^n ...
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1answer
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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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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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1answer
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Does in this case exist necessarely an eigenvalue equal to $0$?

I pasted more than I refer, hoping to be more clear. Look at the claim of the theorem: it states we can change coordinates untill we reach a "good" form for the equation of $r$, which defines the ...
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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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1answer
19 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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3answers
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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 ...