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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3answers
260 views

Find 3rd and 4th co-ordinates for a square given co-ordinates of two points?

To construct a square we need 4 points . In my problem 2 points are given we can find 3rd and 4th point . e.g. A (1,2) B(3,5) what should be the co-ordinate of 3rd (C) and 4th (D) points . Please ...
0
votes
1answer
161 views

Using an offset data point with x, y coords to find the true centre of a circle

I have a data point at (0, 0) where measurements of a tank's shell are taken from. I have used this data point to plot the circle in a graph. However, this data point is not the true centre of the ...
2
votes
1answer
154 views

Is there an efficient way to prove orthogonality of a coordinate system?

Suppose we define a new orthogonal coordinate system, such as spherical coordinates defined by $$x = r \sin \theta \cos \phi, y = r \sin \theta \sin \phi, z = r \cos \theta.$$ Is there an efficient ...
-1
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1answer
29 views

$12x^2 +7xy -py^2-18x+qy+6=0$ represents a pair of $\perp$ straight lines. Find $p$ and $q$. [closed]

I'm sorry I can't show you what I've tried because I don't know how to start. For those who start from behind: p=12,q=1. Any help would be appreciated. :) thanks.
2
votes
2answers
1k views

Find the equation of the locus of a point which has its sum of distance from (0,3) and (0,-3) equal to 8.

I know the answer but due to various expressions under root, I'm unable to reach there. Is there something which I'm missing to make the solution easier? By the way the answer given is ...
0
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2answers
68 views

What is this kind of geometry called?

I want to get Cartesian coordinates of the points of a curve (e.g. a bezier curve) based on the distance (e.g length of the arc) from the start point on the curve. To make this more clear, suppose I ...
2
votes
2answers
3k views

How to rotate a vector by 90 degree?

Suppose I am given a vector in 2-D as $AB = {(x_1,y_1) ,(x_2,y_2)}$. Now , what will be the co-ordinates if I rotate the vector about the point $(x_1,y_1)$ both clockwise and counter-clockwise ?here ...
1
vote
1answer
50 views

Finding circumcenter

In a triangle A(1,2) B(2,3) C(3,1) and $\angle A = cos^{-1}(4/5)$, $\angle B = \angle C = cos^{-1}(\frac{1}{\sqrt{10} }) $ Ordinate of circumcentre of the $\triangle$ is ? I have tried solving by ...
0
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1answer
29 views

Find the co-ordinates of the point on the curve

Calculate the points on the curve $y=(1-x)^4$ at gradient = -4 I solve little bit $\frac{dy}{dx} = 4(1-x)^{4-1}\cdot \frac{d}{dx} (1-x)\\ = 4(1-x)^3 \cdot (-1 )$ the gradient is =-4 so I put ...
0
votes
2answers
380 views

double integral over an arbitrary triangle

Assume we have an arbitrary triangle ABC in x-y plane and we want to integrate a function $f(x,y)$ over surface of this triangle as shown in fig. 1: We can define another coordination system [x' ...
0
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1answer
19 views

When to use transformation of variable and when transformation of differentials

I was reading the book: Mathematical Methods in the Physical Sciences by M. Boas and I came across this statement; I wasn't quite sure why this was the case. Is it because in the curvilinear ...
1
vote
1answer
738 views

Reaching a point B in Cartesian coordinate via Euler angles knows its initial point A Euler angles and Cartesian coordinates

I have a point A:- Known it's Cartesian coordinates (X,Y,Z) and its Euler angle Aka body rotation (R,P,Y) respectively Roll (rotation around X axis) , Pitch (rotaion around Y axis) and Yaw (rotation ...
1
vote
1answer
25 views

Find a change of coordinates matrix

Find the change of coordinates matrix that changes coordinates in the basis $1$, $1+t$ in $P_1$ to the coordinates in $1-t$, $2t$.
2
votes
4answers
131 views

locating any point on a real number line

So my question is really simple (and may be a bit naive): The claim is, I can locate any point in a 2D-plane by recursively applying the following method (possibly infinite number of times): For ...
-1
votes
2answers
51 views

Prove radius chord theorem without using congruent traingles

Suppose that $P(a,b)$ and $Q(c,d)$ are two points on the unit circle $x^2 + y^2 = 1$, and let $M$ be the midpoint of chord $PQ$. (Without using congruent triangles), prove that $OM$ is perpendicular ...
1
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0answers
24 views

Insert Coordinate into best place within list of coordinates in a route

I have a list of coordinates: ...
2
votes
3answers
322 views

Explanation of formula for distance between triangles in a triangular grid

Lets say you have a triangle similar to the one below, with each triangle numbered $(N, i) $ where $N$ is the row number and $i$ is the position within the row. From any triangle, you are allowed ...
0
votes
1answer
28 views

Show P, Q and R are non collinear

If P $\equiv$ $(-sin(\beta - \alpha), -cos\beta)$, Q $\equiv$ $(cos(\beta - \alpha), sin\beta)$ and R $\equiv$ $(cos(\beta - \alpha + \theta), sin(\beta - \theta))$, where $$0 \lt \alpha, \beta, ...
2
votes
3answers
222 views

How to determine if a triangle can be drawn with the given points.

Given $3$ points $$(x_1, y_1), (x_2, y_2), (x_3, y_3),$$ how does one determine whether they are vertices of a triangle? Thanks.
0
votes
1answer
32 views

A basic relation in spherical coordinates

Why is it that $$x\partial_x+y\partial_y+z\partial_z=r\partial_r~?$$ I know that $$r^2=x^2+y^2+z^2,$$ but how is this relation implied?
0
votes
2answers
1k views

equation of circle tangent to line with radius

Find the equation of a circle tangent to line $3x + y - 2 = 0$ at $(-1,5)$ and with radius $\sqrt{10}$. I've no idea on how to do this.
0
votes
1answer
668 views

Transformation from cartesian to polar Coordinates of Vector Field

This is fairly low-level, still I would like to get a verification: I vector field $$\mathbf{F}=F_x \hat{e_x} + F_y \hat{e_y} = F_r \hat{e_r} + F_{\phi} \hat{e_\phi}$$ given in cartesian coordinates, ...
1
vote
1answer
6k views

How to find coordinates of 3rd vertex of a right angled triangle when everything else is known?

I want to locate precisely the 3rd coordinate of a right angled triangle. I have: the length of three sides The three angles The other two coordinates of the triangle The triangle can lie in any ...
2
votes
1answer
1k views

Difference between the Jacobian matrix and the metric tensor

I am just studying curvilinear coordinates and coordinate transformations. I have recently come across the metric tensor ($g_{ij}=\dfrac{\partial x}{\partial e_i}\dfrac{\partial x}{\partial ...
1
vote
1answer
35 views

Projecting coordinates on to X,Y grid

I have some coordinates, [x,y] top left corner, and [x,y] bottom right corner, I want to calculate these in relation to a grid which is 600 * 585 So. -8200,8150 = ...
0
votes
1answer
33 views

Coordinate change

I am working on a problem that asks me to find the equation for the ellipse with foci $(1,1)$ and $(-1,-1)$ and passing the point $(2,2)$. So I went ahead and did the coordinate change, in which case ...
3
votes
2answers
1k views

What is the number of integer coordinates on a line segment?

What is the number of integer coordinates(end points included) on a line segment with integer end coordinates $(x_1,y_1)$ and $(x_2,y_2)$? Integer coordinate means that both abscissa and ordinate are ...
0
votes
0answers
49 views

Intermediate vector naming convention when converting 3D Vector to Spherical Coord

Given the "Red" arrow as the vector of interest in the image below, is there a standard (or practical) name for the "Blue" vector? This is for the purpose of naming variables/methods related to the ...
-2
votes
1answer
102 views

The locus of points with given sum of squares of distances to two fixed points

$A(a,b)$ and $B(b,-a)$ are two fixed points. If $P(x,y)$ is a moving point such that $$|AP|^2 + |PB|^2 = |AB|^2 \tag1$$ prove that $x^2 + y^2 =(b-a)(x+y)$. So far I tried to use distance formula ...
1
vote
1answer
766 views

Longitude and latitude problem

I find this question challenging. I am trying to solve this question for my younger brother. So here it goes: An airplane leaves an airport $X$, 20.6$^0E$ and 36.8$^0N$, and flies due south along the ...
0
votes
1answer
37 views

Area Of Polygon Whose Edges Are In Given Distance From A Given Polygon Edges

I'm handling a problem which I find quite difficult to solve; My input is a changing number of coordinates (real GPS coordinates), usually I get 4-8 coordinates, and another number,which indicates a ...
0
votes
2answers
3k views

How to find a vector normal to a cylinder in cylindric coordinates?

I'm trying to solve a problem which demands to multiply a vector M and vector normal to a cylinder's surface in cylindric coordinates. Height of the cylinder is infinite and its radius is R. So how do ...
2
votes
0answers
386 views

Finding the leftmost, rightmost, top, and bottom, points, on a surface, of a sphere.

So I'm making a 3D game, and the player is inside a glass sphere. I'm projecting a bunch of points onto the sphere, and I need to find the leftmost, rightmost, topmost, and bottommost points, so I can ...
1
vote
0answers
18 views

Add a rotation to latitude/longitude -> screen coords?

I found an algorithm which allows to convert latitude/longitude to (x, y) of a screen. The problem is a picture on a map is rotated. If it is not rotated then I use the following calculations: ...
9
votes
1answer
3k 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 ...
0
votes
2answers
197 views

What is the y-cooridinate for the point on the curve with x-cooridante 20?

What is the y-coordinate for the point on the curve with x-coordinate 20? $F. 160$ $G. 162$ $H. 164$ $J. 166$ $K. 168$ The explanation says "The correct answer is G. If the x-coordinate is 20, ...
0
votes
2answers
58 views

Spherical coordinate versor problem

I have to calculate $$ i_\rho \times i_\phi $$ it should be $$ i_\theta $$ but in my notes I have $$ - i _\theta $$ Which one is correct? How can I do this kind of operations without mistakes?
1
vote
2answers
3k views

Finding the points where a circle intersects an axis

A circle has the equation: x²+y²+4x-2y-11 = 0 What would be the coordinates of the points where the circle intersects with the y-axis and how would you calculate it?
4
votes
1answer
189 views

Changing local coordinates on a manifold by a diffeomorphism

This is the set up of my problem: Let $M$ be a manifold with local coordinates $x^1,\dots, x^n$. Let $x^1,\dots,x^n,\xi_1,\dots,\xi_n$ denote the induced coordinates on $T^\ast M$. Let $f:M\to M$ be ...
1
vote
0answers
112 views

Cartesian to geodetic conversion of 3D bounding box - How to calculate latitude and longitude from an axis aligned bounding box

I have a geometry with its vertices in cartesian coordinates. These cartesian coordinates are the ECEF(Earth centred earth fixed) coordinates. This geometry is actually present on an ellipsoidal model ...
9
votes
3answers
3k views

Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane.

I read this formula in some book but it didn't provide a proof so I thought someone on this website could figure it out. What it says is: If we consider 3 non-concurrent, non parallel lines ...
0
votes
1answer
98 views

Latitude and longitude to screen coordinates using “mapping points”?

I wrote a simple application which has a static image. I have 2 types coordinates for a point (or points if it is necessary): latitude and longitude; x and y for a screen. So I can get some ...
2
votes
0answers
113 views

Transition Functions for Cartesian Coordinate Systems

This is my first time using Mathematics SE (I've only used Physics and Astronomy before), so I apologize if this question is awkwardly phrased or incorrectly presented. I welcome any and all edits and ...
2
votes
3answers
104 views

Manifolds, charts and coordinates

Let's consider the manifold $S^1$ It is well known that we need two charts to cover this manifold. Nonetheless, we can cover the full space using a single coordinate $\theta$ which is just the angle ...
0
votes
1answer
49 views

Counting points in/on cuboid

Given a cuboid that extend in x,y,z axis such that |x|≤N, |y|≤N, |z|≤N where N is given and can have value up to 10^9.Now a shooter is standing at origin (0,0,0).He need to shoot on any of the ...
2
votes
1answer
44 views

Changing the length scale of the system of coordinates

Change the length scale on the axes of original system of coordinates, in which the equation $$y=x^3-px\qquad\text{(1)}$$ is plotted, i.e. introduce new coordinates $x_1$ and $y_1$ instead of ...
3
votes
2answers
77 views

Can a straight line be drawn from origin to co-ordinate X,Y?

Given a co-ordinate P(X,Y), can a straight line be drawn from origin to P, if there is wall existing with end points A(X1,Y1) and B(X2,Y2)? My Approach: I first of all wrote the equations from origin ...
1
vote
1answer
110 views

Solid angle subtended in latitude-longitude maps

I need to scale a latitude-longitude map with the solid-angle each "pixel" subtend. How can I obtain the said solid angle starting from the $\phi$ and $\theta$ angles? Thank you very much
1
vote
1answer
135 views

How to find the angle between two vectors?

Here, I would like to describe my requirements .. Let's say we have two vectors named $\bf A$ and $\bf B$. Two vectors are in different magnitude and opposite directions and lay on different planes. ...
3
votes
1answer
107 views

True or False. Non parallel lines in 3-space.

Two non parallel lines in 3 space must intersect in at least one point. True or False? I say false because you can have two perpendicular lines on x and y, but on a different "level" of the z-axis. ...