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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0
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1answer
332 views

Find a locus of points to satisfy these conditions?

So, we have to straight lines: $$3x-4y+5=0$$ $$2x+3y-4=0$$ You have to find a locus of points from which all perpendiculars to the two lines given are in a 2:3 ratio.
3
votes
2answers
706 views

Quick question regarding coordinate geometry

Note: My exam is in about 1 hour and i just realized that i have a unsolved paper, this is one of the questions that i wasn't able to answer from it. I would highly appreciate it if a full explanation ...
4
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3answers
392 views

Two questions for coordinate geometry

Note: I am burning through dozens of questions from sample papers and these i couldnt understand, these are not homework and i would appreciate it if the full answer could be provided. The first ...
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0answers
57 views

Linear 2D transform in the sense of geometric figures?

Consider tranformation which turns one aligned rectangle to another: This tranformation can be written in matrix form in the following way where ...
0
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1answer
1k views

How to apply transformations to line equation?

I use line equation of style $y=a*x +b$ , I want to apply transformations (rotation, translation in $x$ and $y$) on the line without changing the form by only changing the $a$ and $b$, I know for ...
1
vote
1answer
213 views

triple integral - ecliptic coordinate

I need to find the $V$ by triple integral. the limits from up is (1) - ecliptic cone. and from dwon - (2) - elepsoide. $$(1) \ \ \ \ z=-\sqrt{3x^2+5y^2}$$ $$(2) \ \ \ \ {3 \over 10}x^2+5y^2+{z^2 ...
0
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1answer
2k views

Angle between two coordinates(latitude, longitude) from a position on earth

Suppose I am standing at latitude, longitude $(-33, 151)$ and I want to calculate the angle between two points $(-32, 150)$ and $(-34, 152)$ from my point of view. Can someone please tell me how can I ...
2
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3answers
78 views

Find at least two ways to find $a, b$ and $c$ in the parabola equation

I've been fighting with this problem for some hours now, and i decided to ask the clever people on this website. The parabola with the equation $y=ax^2+bx+c$ goes through the points $P, Q$ and $R$. ...
1
vote
1answer
153 views

Change of coordinate matrices

Find the change of coordinate matrices: Wherein B is the standard basis for P2 $$B' = (t^2+2,t+3,t^2+t+1) \\B" = (2t^2+t+1, t^2, 2t+1) \\ B= (t^2,t,1) $$ $$P_{B'B}$$ means the transformation for the ...
0
votes
1answer
158 views

Transformation of a matrix, change of basis

Find the change of coordinate matrices: Wherein B is the standard basis for P2 $$B' = (t^2+2,t+3,t^2+t+1) \\B" = (2t^2+t+1, t^2, 2t+1) \\ B= (t^2,t,1) $$ $$P_{B'B}$$ means the transformation for the ...
0
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1answer
726 views

get position of point given distance from other points?

I have a 2 points i know the distance between them with a 3rd points. how to get the position of the 3rd point given other distances with the other two points ?
2
votes
2answers
112 views

question on transformation

If a $2$d coordinate transformation function is given by $f(x,y)= 3x+1$, then what does it mean? How do I calculate the transformed coordinates for the points say $(3,4)$ in the initial space?
2
votes
1answer
190 views

A Question About Linear Interpolation

So lets say I have two points $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$. $A$ and $B$ are each associated with some scalar value $K_1$ and $K_2$. $K_1$ is negative and $K_2$ is positive and all the ...
1
vote
1answer
226 views

Test of handedness

I'm reading a book on linear algebra, where the author gives a method to test the handedness or chirality of a given set of 3 basis vectors. if (v1 x v2) . v3 > 0 then it's right-handed, while if ...
2
votes
2answers
3k views

Finding a coordinate vector for specific basis

I am having trouble with a specific problem concerning coordinate vectors. I have a basis $B' = \{t^2 + 2, t + 3, t^2 + t + 1\} $and a polynomial $p(t) = 4t^2 - t$. so I believed the way to go about ...
0
votes
0answers
32 views

Coordinate System in three dimensional system

I want to ask about the formula to find the height of an object with respect to the another object's position using the $x, y$ and $z$ coordinate system. Like, I am making a game and it has terrain ...
3
votes
3answers
602 views

Tetrahedron problem (proving)

Prove that if $P$ is the intersection of the altitudes of a tetrahedron $ABCD$ and $r$ is the circumradius then $PA^2+PB^2+PC^2+PD^2=4\cdot r^2$.
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1answer
152 views

Reflecting a Point about a Line

I am looking for the abstract concept of rotating a point repeatedly. Equilateral triangle ABC has vertices (0,0), (2,0), (1,$\sqrt{3}$). If in an equilateral triangle ABC we take point X to be the ...
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2answers
133 views

Coordinate system conversion: what it is called what I'm doing?

I want to do a simple coordinate transformation and would like to know what is the rigorous way to describe this mathematically in order to be able to search for algorithms for more complex ...
2
votes
1answer
1k views

Find coordinates of equidistant points in Bezier curve

I have to find points (say 10 points) in Bezier curve with 2 control points such that they are at equidistant positions in the curve. Currently I am using the following formula which gives me points ...
2
votes
1answer
465 views

How to get Euler angles with respect to initial Euler angle

I have a sensor which gives me Euler angles (roll,pitch,yaw). There is a baseline value of Euler angle (assume it is $5,10,15$) at the beginning.I want to calibrate from this baseline values all ...
2
votes
2answers
94 views

find point on edge of rect between two points

If I have a rectangle { x = 25, y = 135, width = 30, height = 15 }, and a random point { x = 235, y = 320 }, how can I find the point along the edge of the rectangle that is between the center of the ...
0
votes
1answer
135 views

Determining direction based on (x,y) coordinates

I am making a $2D$ game where an enemy shoots a fireball at the player. Both the player and the enemy have $(x, y)$ positions and are capable of facing in $8$ directions: UP, DOWN, LEFT, RIGHT, ...
0
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1answer
77 views

Burgers equation change of variable

In this paper on the Burgers equation (1.1), $$ u_t = \left(\nu u_{xx} - \sigma u^2\right)_x, $$ the authors use a simple change of variables (2.1a,b) $$\begin{align} u(x,t) &= q(y,t) \\ x ...
2
votes
2answers
320 views

Find parametric expression of an arc given its start point, end point and central angle in 3D cartesian coordinate system

In a 3D cartesian coordinate system, the coordinates of start point and end point have been given as $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. If the central angle of the two points (the one smaller ...
0
votes
1answer
30 views

Affects of a coordinate transformation

I am attempting to solve a PDE of $f(r,t)$, where $r\in[0,g(t)]$ is a spacial coordinate and $t$ is time. The PDE is coupled to to an ODE for $g(t)$. I wish to simplify the problem by defining a new ...
0
votes
1answer
364 views

How to determine a Triangle vertices by its coordinates?

I have to solve this problem, yet I'm not sure what is asked. Given a triangle whose vertices are defined by its coordinates. Determine where is the point O with the given coordinates - inside or ...
0
votes
1answer
241 views

transformation between square and a polygon?

I have a square and a polygon. I want to transform all the points inside this square such that they are mapped inside the polygon. I was trying using scale and rotate matrices but I am not able to ...
1
vote
1answer
312 views

Triangle and parametric coordinates

I'm studying on a book where it says: "A triangle is the set of points where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates ...
0
votes
1answer
337 views

How do I calculate a position in front of a quaternion given the initial position and the quaternion?

Well I want to determine the position in front of, lets say 'an object'. 'An objects' has a position (pX,pY,pZ) and a quaternion rotation (qX,qY,qZ,qW) (where qW seems always to be ...
3
votes
4answers
2k views

How do I determine if a point is within a rhombus?

I know the coordinates of the 4 rhombus' vertices. I also have the coordinates of another arbitrary point (the result of a click on the screen). How do I determine if that point is within the ...
3
votes
4answers
1k views

Why do we draw the $xyz$ coordinate system like this?

Usually people (including, for instance, Calculus teachers) draw the $xyz$ coordinate system in such a way that the $y$ and $z$ axes are perpendicular to each other: Imagine I actually got three ...
0
votes
1answer
127 views

parabola in homogeneous coordinates

So if I have the parabola Y = X^2, how do I go about representing this homogeneously? I know I can parameterize it as F(t) = (t, t^2), but then what? The reason I ask is because I have a 3*3 matrix ...
3
votes
1answer
106 views

Unusual function format and its partial derivatives.

I came across a function of this format: $z = f(u,v)$ where $u = x^2y^2$ and $v = 5x + 1$ Because this function is not in the same format of the ones I've seen before (explicit or implicit), I don't ...
0
votes
2answers
109 views

Turning text-strings into (Cartesian) graphs

A friend told me of a neat site that could turn a text string into an equation for plotting that string, but he forgot to bookmark it. Various web searches haven't helped (the more obvious terms like ...
0
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1answer
84 views

Find base from unit vector code - why changing sign?

I have the following code which accepts a v1 vector and outputs two other vectors to construct an orthonormal base ...
1
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1answer
164 views

Finding the rotation transform between coordinate frames in 3-Space given 1 point

I would like to find the rotation transform between two 3D Cartesian coordinate frames knowing only the magnitude and direction of a single vector shown in both frames. The vector passes through the ...
2
votes
3answers
1k views

The area of the triangle with vertices $(3, 2), (3, 8)$, and $(x, y)$ is $24$. What is $x$?

The area of the triangle with vertices $(3, 2), (3, 8)$, and $(x, y)$ is $24$. A possible value for $x$ is: a) $7$ b) $9$ c) $11$ d) $13$ e) $15$ Please show your work and explain.
0
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3answers
85 views

Doubt on subspace of a vector space

I am new to linear algebra and I have a doubt that : in 2D coordinate system is a line which is at 45 degree NOT passing through the origin a subspace of the vector space comprising the whole 2D plane ...
1
vote
2answers
327 views

Half distance between two points in space

Given two points $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$ on the tridimensional space how can I get the coordinates of the point located exactly on the half of the distance between the two points?
3
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0answers
76 views

Is a solution to some partially differential equation homeomorphic (or diffeomorphic) to a solution of an equation with a different covariance group?

Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
1
vote
1answer
288 views

Finding coordinate vector

The coordinate vector of: $$ \begin{pmatrix} 1&2&-1\\0 & 0 & 6 \end{pmatrix} $$ with respect to the standard basis of $M2x3$ would be: Are you just finding the inverse of this ...
0
votes
2answers
304 views

How to move vector(points) coordinates, for a certain angle

I tried several things, but none worked as it should. How to move vector(points) coordinates, for a certain angle that I calculated! I calculated $\beta = 88.7^\circ$. I'd like to expand/skew vectors ...
2
votes
1answer
241 views

Connection between covariant derivative and basis vectors.

I read here, Curvilinear page 11, that $$\frac{\partial}{\partial x^i}e_j=\Gamma^k_{ij}e_k$$ where the $e_i$'s are basis vectors. There seems to be some connection, but when I calculate it, for ...
0
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3answers
270 views

Equation of a line in homogenous coordinates given 2 points in affine coordinates

So if I have 2 points $A$ and $B$ such that $F(A) = (1; a, a^3)$, and $F(B) = (1; b, b^3)$. how do I find the equation of this line in homogeneous coordinates? So I know how to get a line the ...
1
vote
1answer
131 views

How to map points in a unit square to a regular polygon?

I have a set of points in a unit square $x = [-1,1]$ and $y = [-1,1]$ and I want to remap them to their equivalent points in a regular polygon ($n \geq 3$; Triangle and so on). I've found a really ...
0
votes
1answer
120 views

Find two points across diameter a circle, based on a known position and an isosceles triangle produced from these three points.

I want to find two points across diameter a circle, based on a known position and an isosceles triangle produced from three points that I'll describe as a (the known position) and b and c ( the ...
2
votes
0answers
232 views

Proper name for Inverted Cartesian coordinate system?

In most 2D computer graphic rendering applications (HTML Canvas, Flash, etc...), the coordinate system used is like this: My question is, what is the mathematical/technical name for this kind of ...
1
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3answers
123 views

Symmetry in the line $x=y$

In the plane, why does the symmetry in the line $y=x$ sends the point of coordinates $(x,y)$ into the point of coordinates $(y,x)$ ? P.S. : does someone have a proof without linear algebra ?
3
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1answer
749 views

Calculate 'Rectangle' Coordinates Given 2 Points and width

I want to create a rectangular polygon using two points as guides. So let's say a journey starts in Egypt and ends in London, my polygon should have 4 points: 10 miles further from London ...