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 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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0answers
8 views

Orthocenter of triangle given by vectors in $3$-dimensional space [on hold]

Given: $B=(1,0,0), D=(0,1,0), E=(0,0,1)$. Question: find the coordinates of the orthocenter $L$ around triangle $BDE$. With the formula used
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1answer
21 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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27 views

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

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 ...
2
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1answer
55 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
8 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
26 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
22 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
23 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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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
10 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
35 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
6 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
16 views

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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0answers
16 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
23 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
24 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
19 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
28 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
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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0answers
14 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
41 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
27 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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0answers
12 views

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
25 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
23 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
48 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
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
26 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
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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54 views
+50

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
22 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
37 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
57 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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0answers
26 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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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
38 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
40 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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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
41 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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0answers
16 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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2answers
26 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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0answers
24 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
23 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
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
20 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
26 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
20 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
15 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 ...