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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3answers
440 views

A triangle has side lengths 4,6,8. A tangent is drawn to incircle parallel to side 4 cutting …

Problem : A triangle has side lengths $4,6,8$. A tangent is drawn to incircle parallel to side $4$ cutting other two sides at M and N, than length of MN is (a) $\frac{10}{9}$ (b) $\frac{20}{ 9}$ ...
2
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3answers
60 views

What separates rotations from other co-ordinate transformations?

I am confused about some seemingly elementary ideas. From what I have understood, a rotation is just a specific class of co-ordinate transformations. If this is true, what exactly separates a rotation ...
2
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1answer
32 views

Approximate sector between two lines?

I need to approximate a red figure. I know coordinates of three points (little transparent circles). I also know a count of segments I need to divide this figure. The angle may be from 0 to Pi and ...
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2answers
161 views

Using the Invariant Principle to prove a coordinate can't be reached

Problem: A robot wanders around a 2-dimensional grid. Starting at $(0, 0)$, he is allowed 4 different kinds of steps: $(+2, -1)$ $(+1, -2)$ $(+1, +1)$ $(-3, 0)$ He is trying to get to $(0, 2)$. ...
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1answer
62 views

Given the coordinates of two of three collinear points such that $PM=MQ$, find the third point

P,M and Q are three collinear points and PM=MQ. If P is the point (-1,4) and M is the point (5,8), find the coordinates of the point Q. What I've Done: I've found the distance MQ which is ...
1
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1answer
96 views

Find functions such that under the Cartesian coordinate system $F(x, y) = f(x) g(y)$ but under the polar coordinate system $F(x, y) = h(r)$.

Find all non-constant function $F(x, y)\in C^2(\mathbb{R}^2)$ such that under the Cartesian coordinate system $F(x, y) = f(x)  g(y)$ but under the polar coordinate system $F(x, y) = h(r)$. My ...
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2answers
107 views

Can you transform any coordinate from any “space” to another “space” that's defined?

This question pertains to Matrix Transformations. So to provide an example, if I have 3D coordinates where $X = -1$ to $1$, $y = -1$ to $1$, $z = -1$ to $1$. They are "normalized" in my mind. Can I ...
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1answer
104 views

Perpendicular at a defined distance from point on line intersects another line in coordinates?

It approximately looks like the following picture The figure may be rotated at any angle. I know the coordinates of points $A$, $B$, $C$, $D$ and the length of $BF$. $\angle ABD$ and $\angle CBD$ ...
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5answers
359 views

Help in question related to locus of pair of tangent to a circle?

This the question in my text-book The tangent to $x^2 + y^2 = a^2$ having inclination $\alpha$ and $\beta$ intersect at $P$. If $cot\alpha$ + $cot\beta = 0$, then the locus of $P$ is : i really ...
6
votes
1answer
520 views

Minimum number of lines covering n points

Let there be n points in the plane. I want to know the minimum number of horizontal and vertical lines covering all the points in the plane. My initial approach started like this, 1) for each point I ...
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0answers
53 views

Linejoin for fat lines?

I draw a figure with 2 fat lines. I need to draw a join between these lines correctly. Long red lines are in a middle of each fat line. What I know: coordinates of white points. the angle between ...
0
votes
2answers
406 views

Converting $(4,-4{\sqrt3}, 6)$ from rectangular to cylindrical coordinates

I'm getting the wrong answer for $\theta$. What am I doing wrong? $$(4,-4{\sqrt3}, 6)$$ $$r =\sqrt{4^4 + (-4\sqrt{3})^2} = 8$$ $$z = 6$$ $$\tan\theta=\frac{-4\sqrt{3}}{4}$$ $$\tan\theta=-\sqrt{3}$$ ...
18
votes
6answers
28k 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 ...
1
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1answer
232 views

Perpendicular unit vectors

I have a known unit vector $p (a,b,c)$. First I want a unit vector $q$ which is perpendicular to $p$ and passing through a known point $V(X_0,Y_0,Z_0)$. Then a another unit vector $r$ which ...
3
votes
1answer
60 views

Cauchy-Riemann equations in arbitrary coordinates?

The CR equations in rectangular coordinates can be written as one equation in the following way: $$\frac{\partial f}{\partial x} = \frac{1}{i} \frac{\partial f}{\partial y}$$ Likewise, in polar ...
0
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1answer
31 views

Calculate $x_1$ $x_2$ $y_1$ $y_2$ from center coordinates,height and width

What i have here is a rectangle or square.I have the center coordinates $x$,$y$, width and height.How do i go about finding the $x_1$, $x_2$,$y_1$ and $y_2$ from these.
1
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1answer
98 views

show that the straight lines $(a^2-3b^2)x^2+8abxy+(b^2-3a^2)y^2=0$ form with the lie $ax+by+c=o$ an equilateral triangle

show that the straight lines $(a^2-3b^2)x^2+8abxy+(b^2-3a^2)y^2=0$ form with the lie ax+by+c=o an equilateral triangle whose area is $\frac{c^2}{\sqrt{3}(a^2+b^2)}$ is there any other way to solve ...
0
votes
2answers
303 views

equation representing 2 straight lines

Let us assume this equation is given to us we have to factorize it $$12x^2 +7xy-10y^2+13x+45y-3=0$$ By solving we get that this represents two straight lines. But how to factorize it? Is there a ...
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4answers
247 views

How to find equation from points

I have a list of 218 points. Is it possible to find an equation for a line that passes through the points? Update : Is there a software that can generate the equation from the points?
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3answers
500 views

Straight line problem : Find the number of points which lies between the figure : $(0,0) , (0,21); (20,0)$

Problem: Find the number of points which lies inside the triangle : $(0,0) , (0,21); (20,0) $ Approach : Let us take point $A = (0,0)$, $B = (0,21)$, and $C = (20,0)$. Since the figure ...
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1answer
165 views

How to project 3D plots on a 2D coordinate system without losing the metric scale?

I've been collection data of a river bank last week and I need to plot the cross sections of the data. The issue is, that the data taken consists of 3 coordinates: easting, northing and elevation. ...
2
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1answer
99 views

Find direction, angle or co-ord of unknown vertices using only distance?

My current issue is that I have a triangle, where I know all the line distances as well as an origin coordinate. Is there any way I can then gain the coordinates of the other vertices with this ...
1
vote
1answer
547 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 ...
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1answer
379 views

Given 2 points/coordinates, how do I express in $ax + by + c = 0$ form?

Given 2 points eg. $(x_1, y_1), (x_2, y_2)$ how do I express in $ax + by + c$ form? I am supposed to find the intersection of 2 lines. I have 2 points for 1 line, and the other line will be ...
0
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1answer
153 views

locus difficult

A fixed point is at a perpendicular distance a from a fixed straight line and a point moves so that is distance from the fixed point is always equal to its distance from the fixed line.Find the ...
2
votes
1answer
197 views

Find the locus of the point which divides segment AB internally in the ratio 1:2.

A and B are variable points on X and Y axis respectively,such that l(ab)=4.Find the locus of the point which divides segment AB internally in the ratio 1:2. I think that it must be a circle . or ...
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1answer
127 views

Cylindrical coordinate system

Let us consider a fixed reference point P and another point Q in space. Suppose you want to express the position of Q with respect to P in cylindrical coordinate system. Now in the cylindrical ...
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0answers
100 views

Parameterizing a spherical cap in cylindrical coordinates

In calculating the mean curvature for a surface of the form $(f(z)\cos(\theta), f(z)\sin(\theta), z)$ I need to use some checks to ensure I haven't made any mistakes along the way. The one I would ...
3
votes
1answer
148 views

Are cartesian coordinates “more fundamental” than other coordinates, and are they inherently tied to $\mathbb R^n$?

Are the Cartesian coordinates more "fundamental" than other coordinate systems? When someone says $\mathbb R^n$ do we implicitly mean the set of points PLUS Cartesian coordinate system? Sometimes I ...
2
votes
1answer
36 views

coordinate of shorter line

If I have a line segment with endpoints AB,CD. The length of the line is 5 units. If I make the line shorter (eg. 3 units), and one of the endpoints is still AB, how do I figure out what the new CD ...
0
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1answer
53 views

Geometry finding area problem

A regular 2N -sided polygon of perimeter L has its vertices lying on a circle. Find the radius of the circle and the area of the polygon.
4
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1answer
113 views

Calculate the X,Y values of an ellipse

I guess am confused somewhere. I have the length(l) and breadth(b) of an ellipse enclosing rectangle. I know the center point and the angle(x) that the line makes with the center. I want to know the ...
3
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0answers
83 views

Changing coordinate system with non standard definitions

The standard coordinate transformation to polar coordinates is $$ \begin{cases} x=r\cos(\varphi)\\ y=r\sin(\varphi) \end{cases} $$ with $r\in[0,\infty), \ \varphi\in[0,2\pi)$ The question is whether I ...
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2answers
1k views

How to calculate the coordinates of orthocentre.!!

How to calculate the coordinates of orthocentre.!! I was surfing through the net and got this formula.. $$x-\rm coordinate= \frac{x_1\tan A+x_2\tan B+x_3\tan C}{\tan A+\tan B+\tan C}$$ ...
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0answers
4k views

Converting an equation from cartesian to cylindrical coordinates

This is going to seem pretty basic, but I'm trying to figure out if there is a problem in my homework's text or if it's just not clicking for me. I have to find the volume for the paraboloid $$z = 6 ...
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3answers
80 views

How to find the integral by changing the coordinates?

Let R be the region in the first quadrant where $$3 \geq y-x \geq 0$$ $$5 \geq xy \geq2$$ Compute $$\int_A (x^2-y^2)\,dx\,dy.$$ I tried to use $ u= y-x, v= xy$ as my change of coordinates, but then I ...
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1answer
627 views

How to determine gradient of vector in cylindrical coordinates?

I am wondering how to actually determine the gradient of a vector in cylindrical coordinates. I have seen a lot of websites that just say what the general form is but I cannot seem to understand how ...
5
votes
1answer
260 views

Are spherical coordinates unique orthogonal coordinates on sphere?

Spherical coordinates on unit sphere are defined by the following transformation: $$\begin{cases}x=\sin\theta\cos\varphi\\ y=\sin\theta\sin\varphi\\ z=\cos\theta\end{cases}$$ Are these coordinates ...
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vote
1answer
231 views

sketching regions of three variables

If i had a solid region, V, such that $x^2+y^2+z^2\le9$, $x^2+y^2\le4$, $x\le0$ and $z\ge1$ what would be the easiest method to sketch this region? Can someone run me through steps as how to tackle ...
3
votes
1answer
4k views

Calculate Camera Pitch & Yaw To Face Point

How do you calculate pitch & yaw for a camera so that it faces a certain 3D point? Variables Camera X, Y, Z Point X, Y, Z Current Half Solution Currently I know how to calculate the pitch, ...
0
votes
1answer
46 views

Algorithm to approximate the closest nonlinear formula(funciton) for an arbitrary set of points?

I have a table which concists of XY points (so I have a set of points hehe), where X represents the Velocity and Y the Real World Speed. Those points are not linear. With two points it's easy to ...
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2answers
2k views

Finding a line perpendicular to a line and passing through the intersection of other two lines

So here is the question as in my text book Find the equation of the line through the intersection of $2x - 3y + 4 = 0 $ and $3x + 4y - 5 = 0$ and perpendicular to $6x - 7y + c = 0$ so I ...
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1answer
67 views

Center of Distance

I am given $N$ points in a 2D plane($x$ and $y$ coordinates). I have to find a point in this plane with coordinates $X$ and $Y$ such that: $$\sum_{i=1}^N \max\{|X - A_i|, |Y - B_i|\}\text{ is ...
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1answer
360 views

Which matrix transforms my vector field $F(r,\theta,\phi)$ from cylindrical to spherical coordinates

I am looking for the matrix that I have to apply my vector at the position $(r,\theta, z)$ to in order to get the appropriate vector in spherical coordinates. I am totally okay, if you could give me ...
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2answers
373 views

How to calculate the number of integral points inside an area

How many integral solutions (x, y) exist satisfying the equation |y| + |x| ≤ 4 My approach: I have made the graph after opening the the modulus in the above equation by making four equations. Now ...
2
votes
1answer
389 views

Get 2D direction vector from 1D rotation (for game development)

I am working on a game where my object is supposed to move forward based on it's rotation (the direction it's facing) I tried this: increase object x to cos(rotation) increase object y to ...
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1answer
1k views

Express spherical coordinates with different centers in terms of each other.

Imagine that you have two spheres with a distance $R$ from one center to the other one. Now, it is well known how one would get the cartesian position vector of each point in sphere 1 by using ...
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1answer
72 views

The smallest value of $|a|$ such that the lines $ x = a+m $, $y = -2 $ and $y = mx$ are concurrent

Question If the line $ x = a+m $, $y = -2 $ and $y = mx$ are concurrent, the least value of $|a|$ is (A) $\sqrt{2}$ (B) $2\sqrt{2}$ (C) $2\sqrt{3}$ (D) $3\sqrt{2}$ Solution Since the ...
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0answers
102 views

coordinate transformation and scaling

I have a global coordinate system that I need to transform to a local coordinate system. The new and old coordinate systems are shown below. Using transformation rules, I came with with the ...
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0answers
58 views

What's the mathematical formulation for frames for reference?

In this lecture I've come across an interesting formulation of kinematics and reference frames. When I studied kinematics, the idea of what is meant by a 'frame of reference' was never quite fully ...