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
13 views

Determining third vertex of the right angled isosceles triangle

If A(9,-9), B(1,-3) are the vertices of a right angled isosceles triangle, then the third vertex is?? Here in this question i got stuck to the point that which side is taken as the given coordinates. ...
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1answer
255 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 ...
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1answer
14 views

Given two points, I need to find all of the 'sections' of the graph that the line segment travels through.

What do I mean by "sections"? Imagine a piece of graph paper. Each square bounded by integer horizontal and vertical grid lines is a "section", and is named after its lower left coordinate — (1,1), ...
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2answers
344 views

Jacobian for a Cartesian to Polar-Coordinate Transformation

I have a simple doubt about the Jacobian and substitutions of the variables in the integral. suppose I have substituted $x=r \cos\theta$ and $y=r \sin\theta$ in an integral to go from cartesian to ...
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1answer
349 views

How to show that a line pass through a point?

How to show that a line pass through a point? Two fixed straight line $OX$ and $OY$ are cut by a variable line at the points $A$ and $B$ respectively and $P$ and $Q$ are the feet of the ...
6
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1answer
101 views

Transforming a PDE given basis vectors

I have a non-orthogonal coordinate system defined by $\mathbf x=\mathbf x(r,\beta,z)$, and so I can find the basis vectors as $$ \mathbf g_r=\frac{\partial \mathbf x}{\partial r},\quad\mathbf ...
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3answers
31 views

Coordinate Geometry of triangle question

Can someone please explain how I can get coordinates for B using the slopes that are shown in the question? I'm not sure how I came to my solution where I tried to use y=mx+b. For e.g. to solve for ...
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3answers
75 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
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1answer
496 views

Is the “Constant Rank Theorem” the same as the “Domain Straightening Theorem”? Which theorem is which?

Wikipedia says that the inverse function theorem is a special case of the "constant rank theorem". I'm pretty sure this is supposed to be the same theorem as the "Rank Theorem" on p. 47 of Boothby ...
6
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1answer
253 views

Describing co-ordinate systems in 3D for which Laplace's equation is separable

Laplace's Equation in 3 dimensions is given by $$\nabla^2f=\frac{ \partial^2f}{\partial x^2}+\frac{ \partial^2f}{\partial z^2}+\frac{ \partial^2f}{\partial y^2}=0$$ and is a very important PDE in ...
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1answer
28 views

How to find the velocity and accelaration in a 3d space with 6 degrees of freedom?

I have the following rigid body: I assume that the body is a symmetric cylinder.x,y,z are the axes of the reference frame resulting from a transformation involving three orthogonal rotations ...
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1answer
279 views

Spherical coordinates of a unit vector around a normal $N$

So if I have a unit normal for a surface $N(x,y,z)$ and an incident unit vector $V(x,y,z)$ to that surface, how would I represent the vector V in spherical coordinates relative to the normal?
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1answer
344 views

Rotating a point in spherical coordinates around Cartesian axis

If I have a point in spherical coordinates, and I rotate it around one of the Cartesian axes, what will be the new spherical coordinates for the point? Both spherical and Cartesian coordinate systems ...
6
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4answers
12k views

finding out the area of a triangle if the coordinates of the three vertices are given

What is the simplest way to find out the area of a triangle if the coordinates of the three vertices are given in x-y plane? One approach is to find the length of each side from the coordinates given ...
2
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1answer
85 views

Problem of a circle tangent to three other circles

Two circles with centres A and B and radii 14 and 7 units respectively touch each other externally. M is the mid point of segment DE and is the centre of the circle with radius 21 units. The two ...
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1answer
26 views

Construct a procedure which determines the location of the shadow of a rectangluar box.

I drew a 3d rectangular box on a coordinate plan consisting of x, y, and z. A procedure is to be created that will determine the location of the shadow of the box on one of the coordinate planes. I ...
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1answer
21 views

Determining transformation matrix from six points

Given that I have the locations of three points: p1 = [1.0,1.0,1.0] p2 = [1.0,2.0,1.0] p3 = [1.0,1.0,2.0] ...and I know their transformed counterparts: ...
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0answers
38 views

Intesection point of feet of altitudes

If triangle has vertexes at $(x_1,y_1),(x_2,y_2),(x_3,y_3)$, is the intersection points of feet of altitudes $$x_h = \frac{x_1x_2(y_2-y_1) + x_2x_3(y_3-y_2) + x_3x_1(y_1-y_3) + y_1^2(y_3-y_2) + ...
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2answers
74 views

Finding closest point perpendicular to B

Given: A = 8,4 B = 4,8 C = 4,4 D = ?,? From point C (4,4) (red dot) how would I find the coordinate that would be perpendicular to AB and CD being parallel to ...
2
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1answer
295 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 ...
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1answer
23 views

Solving for $x$ in terms of $y$ using coordinates

A line passes through $(4,1),(1,y),$ and $(x,2)$. What is the value of $x$ in terms of $y$? What equation do I have to use for this problem? $m=\frac{y_2-y_1}{x_2-x_1}$ , $y=mx+b$ , $y-b=m(x-a)$ I ...
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0answers
3 views

Underlying connections between parametric surfaces and co-ordinate transforms

I've recently been learning about parametric surfaces and surface integrals involving various co-ordinates systems. I was wondering, is there a fundamental connection between parametrization and ...
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1answer
250 views

Homothetic transformation

Suppose that, we have a homothetic transformation in a rectangular coordinate system, with center origin $(0,0)$ and $k$. This homothetic sends point $A(2,3)$ to point $B(2x-1,x)$. My aim is to find ...
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2answers
94 views

Number of solutions of a simple equation

Problem How to count the number of distinct integer solutions $(x_1,x_2,\dots,x_n)$ of the equations like : $$|x_1| + |x_2| + \cdots + |x_n| = d $$ the count gives the number of coordinate points ...
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1answer
18 views

Trying to figure out coordinates of isoscleles triangle

I'm programming some application, which heavily depends of geometry. Let's say, in 2D coordinates system I have i.e. : Bxy = (5,-2) Cxy = (2,-5) ABlength = 5.5 ...
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1answer
26 views

Equation Of A Straight Line Passing Through A Point and Having an Intercept

The question is as follows: "Find the equation of the straight line passing through (-2,-7) and having intercept of length 3 units between straight lines 4x + 3y = 12 and 4x + 3y = 3." I really ...
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1answer
26 views

How to find circumference origin position?

I need to find origin of circumference which is defined by two points and vertex angle of isosceles triangle: I've got radius of triangle by ...
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2answers
21 views

Orthonormal basis in a cylindrical coordinate system

So I am supposed to show if these vectors make an orthonormal basis in a cylindrical coordinate system. $\vec e_p=\bigl(\begin{smallmatrix} cos(\theta )\\ sin(\theta )\\0 \end{smallmatrix}\bigr); ...
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0answers
13 views

Minimum and maximum points

The question is : Find the shortest distance from the point (2,1,-1) to the plane : x+y-z=1 . So can we solve this problem by using the rules of stationary points ( minimum points ) , if not , How ...
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0answers
72 views

Elastic wave equation in curvilinear coordinates: how do you perform a coordinate change?

The essence of this question is that I don't know how to convert an equation from Cartesian coordinates into curvilinear coordinates, and would like to know how, preferably using the language of ...
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1answer
28 views

defining a closed curve in cartesian coordinates

I am trying to implement a track in cartesian coordinates, such that X and Y coordinates are accepted and those are linearly interpolated. The problem is, I want to include circular shapes on ...
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1answer
467 views

coordinate geometry - find point in right-angled triangle

I'm making a map. I've come across a geometry problem, and I'm not so knowledgeable about maths! Let me illustrate with pictures. I am trying to plot flightpaths with a curved line, using a ...
0
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1answer
18 views

How do I get the start and endpoint of a line using the middle point and the angle?

I have a line that goes from P1 to P2 in a 2D space. I have the location of the middle point of that line, and the angle of inclination of the line. The thing is that I don't know the length of the ...
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1answer
39 views

Having 2 coordinates putting the third coordinate on the closest 90 degree point

I've got a follow-up question for the previously asked and answered question here What I am trying to do now is that when I have a third coordinate I want it to be converted to the closest point on ...
2
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1answer
114 views

Vector Algebra Coordinate Transformation

Let us look at two coordinate systems $K$ and $K'$ with axes, respectively, $(x_1,x_2,x_3)$ and $(x_1',x_2',x_3')$ and unit vectors ($\vec{e_1},\vec{e_2},\vec{e_3}$) and ...
2
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1answer
19 views

Calculate Coordinates

I have the following two circles (n1, n2). I know the coordinates of them. They are connected with a line. I also know the angle "alpha" and the diameter of the circles. Now I try to calculate the ...
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3answers
83 views

Volume of the solid bounded by the sphere $x^2 + y^2 + z^2 = 9$ and paraboloid $8z = x^2 + y^2$

Find the volume of the solid bounded above by the sphere $x^2 + y^2 + z^2 = 9$ and below by the paraboloid $8z = x^2 + y^2$ I'm having some trouble finding the correct limits of integration in ...
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0answers
59 views

Maximum product of lengths involving secant drawn to a parabola.

A chord is drawn from a point $P(1,t)$ to the parabola $y^2=4x$, which cuts the parabola at $A$ and $B$. If $PA\cdot PB=3|t|$, what is the maximum possible value of $|t|$? All I can infer is that the ...
2
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1answer
51 views

Locus of a point $P$ inside $\triangle ABC$

$P$ is a point inside $\triangle ABC$. $X$, $Y$ and $Z$ are feet of perpendiculars from $P$ on $BC$, $CA$ and $AB$ respectively. Find the locus of $P$ if $XY=XZ$ and $A \equiv (4,3)$, $B \equiv ...
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1answer
34 views

Having 2 coordinates calculating the 90 degree angle formula of the next point

I have 2 coordinates, what would be the 90 degree formula to the next point I am drawing? Say ...
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1answer
22 views

Calculating rectangle having 2 coordinates and 1 length

How could I calculate the other 2 points if I have a rectangle with 2 points and 1 length given? ...
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2answers
23 views

Coordinates of a vector under a basis in a Hilbert space?

Given an arbitrary basis $\{m_1, \dots, m_n \}$of a Hilbert space $H$ (or just think it as $\mathbb R^n$, and I think the methods should be the same) with given inner product, how can we find the ...
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0answers
21 views

How to calculate end point of vector using quaternion?

How can the end-points of the three orthonormal vectors representing local coordinate system of point (p.x, p.y, p.z) be calculated given rotation represented by quaternion in global coordinate system ...
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0answers
48 views

What did homogeneous coordinates allow 19th century mathematicians to do?

I read about Mobius developing Barycentric and homogeneous coordinates, and I read about homogeneous coordinates and what they are and I'm totally on board with taking a line from the origin and ...
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0answers
46 views

Computing area of triangle via equations of medians

For a triangle $ABC$, $B=90^\circ , AC=6$, equations of medians through $A$ is $y=2x+4$ and through $C$ is $y=x+3$. What is the area of triangle $ABC$? I'm really bad at geometry, and to make matters ...
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0answers
12 views

How do I convert between the different co-ord systems for Ray Tracing?

I am having trouble understanding how to convert (and what to convert) for my ray tracing program. At the moment I only have 3D to 2D projection transformation which is used to project the 3D world ...
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1answer
236 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 ...
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1answer
300 views

Family of Straight line : Consider a family of straight lines $(x+y) +\lambda (2x-y +1) =0$. Find the equation of the straight …

Problem : Consider a family of straight lines $(x+y) +\lambda ( 2x-y +1) =0$. Find the equation of the straight line belonging to this family that is farthest from $(1,-3)$. Solution: Let the ...
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2answers
102 views

Find the locus of points M the difference of the squares of whose distances from two given points A and B is equal to a given value c.

Find the locus of points M the difference of the squares of whose distances from two given points A and B is equal to a given value c. For what values of c does the problem have a solution? I am ...
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1answer
20 views

Coordinates change

Lets say our vehicle is moving at $50\frac{km}{h}$ ($31 mph$) for $15$ seconds only on $X$ or $Y$-axis (also on both). How much does the Geographic coordinates change in that time? I googled and ...