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
29 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
59 views

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
53 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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2answers
30 views

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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0answers
38 views

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
67 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
164 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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1answer
50 views

How to obtain a rectangle's side's positions if its origin isn't in its middle?

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
127 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
20 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
52 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
66 views

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
42 views

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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0answers
20 views

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
16 views

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
138 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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0answers
12 views

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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0answers
51 views

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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0answers
27 views

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
30 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
26 views

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
31 views

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
19 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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0answers
24 views

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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0answers
63 views

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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0answers
31 views

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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1answer
42 views

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
30 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
90 views

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
21 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
43 views

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
33 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
40 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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0answers
97 views

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
33 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
38 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 ...
2
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1answer
64 views

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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1answer
30 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
44 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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5answers
2k views

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
48 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 ...
1
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1answer
63 views

Transform from global coordinate system to a local

I have a plane in $\mathbb R^3$, defined by a direction vector $$\vec n= \langle n_x,n_y,n_z\rangle$$ and a point $C(X_1,Y_1,Z_1)$. The direction of the normal unit vector $\vec n$ is described from ...
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2answers
53 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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1answer
44 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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1answer
33 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
29 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 ...
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1answer
27 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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2answers
91 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
23 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
35 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 ...