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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If the diagonals of a trapezoid are congruent, then the trapezoid is isosceles.

Thanks in advance to anyone who can help me out on this. I'm currently a junior in high school taking and doing well my school's honors pre-calc class, but of all of the math I've ever learned, proofs ...
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0answers
81 views

Difficulty understanding the definition of the Barycentric coordinate system

Specifically, the definition at http://en.wikipedia.org/wiki/Barycentric_coordinates_%28mathematics%29#Definition Let $x_1, \dots , x_n$ be the vertices of a simplex in a vector space $A$. If, for ...
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2answers
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Linear equations; how to write an equation from given coordinates?

A straight line goes through the points $( 0, 1 )$, $( 2, 7 )$ and $( 4, 13 )$ and I need to write the equation of this straight line. How do you write equations? I know you have it's usually $y = x ...
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1answer
34 views

Given coordinates of $C$ and $\overline{AC} = \overline{BC}$, find $A$ and $B$.

If $C$ has coordinates $(\sqrt 7, \sqrt3)$ and $\overline{AC} = \overline{BC}$, what are the rational coordinates of $A$ and $B$?
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1answer
76 views

Can one use Pick's theorm to prove that area size 5 covers at least 6 grid points?

According to Pick's Theorem, the size of an area $A$ can be calculated by the sum of the interior lattice points located in the polygon $i$ and the number of lattice points on the boundary placed on ...
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1answer
51 views

What is the name of two points that share one coordinate?

Is there an adjective to characterize two points in $\mathbb R^2$ that have the same value for one of the coordinates?
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59 views

Polar coordinates on a set T

This exercise show that f is a gradient on the set $$T= \mathbb{R}^2-\{(x,y)| y=0, x \leq 0 \}$$ consisting of all points in the xy-plane except those on the nonpositive x-axsis. If $(x,y) \in T$, ...
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1answer
807 views

Coordinate Transformation on Local coordinate system

I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
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2answers
6k views

Don't understand how to use jacobian for transformation of coordinates

Hello. I fail to understand why the Jacobian matrix is used to transform Cartesian coordinates to polar coordinates. If I'm not misunderstanding, it is assumed that the matrix ...
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2answers
2k views

Finding the locus of the midpoint of chord that subtends a right angle at $(\alpha,\beta)$

There is a circle $x^2+y^2=a^2$. On any line that cuts the circle in two distinct points(it is a secant), the points of intersection with circle are taken and at those two points I draw the tangents ...
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1answer
42 views

Creating bounds of a shape

I have a list of coordinates, I need to find the bounds of the points as in a shape where all the points fit into, this shape can be any type of 2D shape (I only have (x, y) no z), as in lets say I ...
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1answer
73 views

maximising the angle $\theta$

OK, suppose I have two points in cartesian coordinate system, say $P(x_1,y_1)$ and $Q(x_2,y_2)$. I have a line as well, that is, for simplicity $$y=mx$$ Assuming that $$y_1\neq mx_1,y_2\neq mx_2$$ I ...
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3answers
480 views

Find coordinates of n points uniformly distributed in a rectangle

I have a rectangle R of width W and height H. I have N points inside this rectangle. I need to find an algorithm to position my points in the rectangle in the most uniform way possible (no overlaps, ...
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1answer
2k views

When to use cylindrical coordinate and when to use spherical coordinate?

so i was told that any kind of 3 space Cartesian coordinate volume question can be solve using rectangular coordinate, cylindrical coordinate and spherical coordinate. Here is the thing, by using one ...
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1answer
245 views

Number of integer solutions of $xy - 6 (x+y)=0$

What are the number of integer solutions of $xy - 6 (x+y)=0$ with $x\leq y$ is ? Equation $xy - 6 (x+y)=0$ can also be written as $1/x + 1/y = 1/6$
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1answer
27 views

Maximal region in the cylindrical space

I would like to determine a maximal region in $(r, \theta, z)$- space which maps injectively into $(x,y,z)$-space Thank you
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2answers
1k views

derivatives transformation

I'm currently doing a calculation for the connection coefficients using the standard space-time coordinates, namely x[0],x[1],x[2],x[3]. The setup is a spherically symmetric problem. In my ...
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1answer
44 views

Euclidean space problem

In three-dimensional space, is it true that if you take line $a$ of a plane and line $b$ of the plane perpendicular to the first one, then the angle between line $a$ and $b$ (at which they intersect) ...
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1answer
4k views

How to find equation of parabola when we only know the equation of latus rectum and coordinates of vertex?

Suppose the equation of latus rectum is x=4 and the vertex is (2,3). I am confused wouldn't there be many parabola with this same vertex and latus rectum.If not how to find the equation? The answer ...
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2answers
187 views

Coordinates of parallel triangle with a distance of 'd' between the parallel edges?

I have a triangle with Co-ordinates $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)\}$. I need to find co-ordinates of a triangle,whose edges are exactly $\alpha$ distance from previous triangle. Below is the figure ...
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1answer
54 views

Solve $x_0 = a\cos(x) + b\cos(x+y-\pi) + c\cos(x+y+z-2\pi)$ and $y_0 = a\sin(x) + b\sin(x+y-\pi) + c\sin(x+y+z-2\pi)$

It has been a while since last time I have tried to solve a trigonometric problem $x_0 = a\cos(x) + b\cos(x+y-\pi) + c\cos(x+y+z-2\pi)$ $y_0 = a\sin(x) + b\sin(x+y-\pi) + c\sin(x+y+z-2\pi)$ Is it ...
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1answer
118 views

Triangle $z$-index interpolation between the vertices

I got a $2$D triangle, each vertex has a $2$D coordinate with a $z$-index value (NOT a $z$ coordinate!). The $z$-index value indicates whether a vertex lays on, in front of, or behind your screen ...
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2answers
39 views

computing the $y_{cm}$

Suppose I have a half disc and the coordinates axes at the centre of base of the disc. For the given system, I have surface mass density $S$ as $$S=S_0 sin\theta$$($S_0$ being positive constant). I ...
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2answers
52 views

Find the tangent to a function

Find the tangent to this $\displaystyle y={1 \over x+3}$ it's crossing the point $(-2,1)$ I have drawn the lines but I can't calculate it
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1answer
214 views

How to handle two-center bipolar coordinates?

In my problem, I want to integrate a 2D function $f(x,y)$ which explicitly depends on the vector $ \vec{r}_1=\vec{r}-\vec{R}_1 $ and $\vec{r}_2=\vec{r}-\vec{R}_2$, where $\vec{R}_1=(a,0)$ and ...
3
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1answer
130 views

Every conic in $\Bbb{P}^2$ equivalent to $XZ - Y^2$ - what is meant by hint here?

I am looking at Miles Reid's UAG book. There he claims that every projective conic is projectively equivalent to $XZ = Y^2$. He asks to show that $Q$ a non-degenerate quadratic form is such that ...
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1answer
45 views

Co-Ordinate Geometry : Please find the mistake

http://i.imgur.com/H59VgOK.png I think there is some mistake in my diagram or the work. Please check the link . The above formula is of Distance Formula(in the link). that is $$\sqrt{(x_2 - x_1)^2 ...
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0answers
91 views

Equation to calculate intersected cells in a grid, given a selection rectangle

I am looking for an equation which will calculate which cells (returned either as a pure index or as a row/col) are intersected by a selection rectangle when provided with the box coordinates of each ...
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0answers
76 views

How to solve a distance problem inside of a picture?

sorry for my bad english. I have the following problem: In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y). Now i want ...
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1answer
339 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.
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2answers
744 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 ...
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3answers
419 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 ...
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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 ...
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1answer
218 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 ...
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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 $R$. ...
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1answer
164 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 ...
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1answer
160 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
757 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 ?
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2answers
113 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?
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1answer
199 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 ...
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1answer
231 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 ...
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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 ...
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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
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3answers
613 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
153 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
136 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
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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
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1answer
481 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 ...