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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Detect Regions Described By Lines in Rectangular Coordinates

Need some help from the superior math minds here. This problem is part of a software project. Essentially, I have a Cartesian grid. The user can create lines by plotting points (every 2 points ...
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1answer
30 views

How can I transform coordinate systems with quaternions?

I have a coordinate system 0 which I'd first like to rotate about its z-Axis which gives me system 1, and afterwards rotate system 1 about its y-axis which gives me system 2. See picture: Both ...
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1answer
27 views

Find the equation of the line.

Find the equation of the line passing through the point $(5,7)$ and parallel to the line $5x+4=0$ If I say $m=5$, how should I find $c$? There is no $y$ in the equation!
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2answers
33 views

Find the equation of the straight line.

Find the equation of the straight line that is parallel to $2y-x=7$ and bisects the line joining the points $(3,1)$ and $(1,-5)$. So, I found the gradient = $\frac{1}{2}$ And I solved the midpoint: ...
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1answer
59 views

Transfer Transformation from Physics to Vector Graphic

Upfront, I am not a professional in Maths and hope that the formulation of my question describes the problem well enough. I am creating a jump'n'run game, which uses a physics engine (Box2D) and SVG ...
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1answer
101 views

How to use geometry to express unit vectors of spherical coordinate system in terms of Cartesian unit vectors

It's quite easy to express unit vector $\hat{r}$ in sum linear combinations of Cartesian unit vectors $\hat{x}$, $\hat{y}$ and $\hat{z}$. But I am not sure how I can use geomtery to find a Cartesian ...
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1answer
46 views

How to find coordinates of a point on a 3D cylinder in Cartesian system if any one point on cylinder and dimensions of cylinder are known?

Consider a cylinder of known dimensions inserted in 3D cartesian space. I know the cartesian coordinate of one point located on the surface of cylinder. Using this information I want to find out the ...
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3answers
42 views

Find the coordinates of $P, Q, R$.

In triangle $PQR$, $A(-2,3), B(5,-1)$ and $C(-4,-7)$ are the midpoints of $PQ, QR$ and $PR$ respectively. Find the coordinates of P, Q and R. I really can't understand how to begin....Please hint :'( ...
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1answer
51 views

Mapping points on a plane in space onto a coordinate plane

Is there a way to isometrically map points on a plane in space onto a coordinate plane? So for example, given the three points $\left( 1,1,0 \right)\;, \left( -1,0,2 \right),\; \text{and }\left( ...
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0answers
64 views

Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
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3answers
47 views

Determining if a point is inside two planes

I have two planes(Plane 1 and Plane 2) the normals ($n_1$ and $n_2$) of which are known to me. How do I determine if a point is inside the two planes? By inside I mean the 3d space between Planes 1 ...
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2answers
33 views

How to find the perpendicular distance from B to AC?

"Find the area of triangle $ABC$ with vertices $A(2, 1), B(12, 2) $and $C(12, 8)$. Hence or otherwise, find the perpendicular distance from $B$ to $AC$." I found the area, which is 30 units by find ...
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3answers
99 views

Find the point on the y-axis which is equidistant from the points $(6, 2)$ and $ (2, 10)$.

Find the point on the y-axis which is equidistant from the points $(6, 2) $ and $ (2, 10)$. Please help, there are no examples of this kind of sum in my book! I don't know how to solve it.
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3answers
74 views

Why are the axes in coordinate geometry perperndicular?

In coordinate geometry, the $x$ and $y$ axis are perpendicular to each other. But is there any special reason for this (other than to make it simple)? Will coordinate geometry have contradictions if ...
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2answers
79 views

Show that the four points given below are the vertices of a rhombus.

Show that the four points, $(5, 8), (7, 5), (3, 5)$ and $(5, 2)$ are the vertices of a rhombus. I tried solving it, by finding out the distances by using the formula $\sqrt{(x_{2}-x_{1})^2 + ...
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1answer
126 views

What do we know about non linear coordinate systems?

I first learned about coordinate systems by Gelfand and I knew that we basically have two axis x and y with origin O and some unit vectors $\hat i$ and $\hat j$ and if $\vec{OA}=x\hat i+y\hat j$ then ...
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3answers
245 views

What is wrong with this method for a rotated and shifted parabola?

$(x+2y)^2=4(x-y)$ Disecting the above parabola is the question. (vertex, axis,tangent at vertex,etc). So at first what I thought of was making its equations at LHS and RHS perpendicular. I thought ...
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0answers
16 views

A method of calculation coordinates in order to implement it to a code language!

lets say that we have three points A(xa,ya,za), B(xb,yb,zv), C(xc,yc,zc) with known coordinates in 3d space. Is there a method to calculate the coordinates (x,y,z) of another point D for which the ...
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0answers
8 views

Given U,V<->X,Y trnslation formula explanation

Well in a text book (about numerical analysis methods to do a polynomial interpolation in bivariate functions). The following piece of text/functions is just given, without much explanation. The goal ...
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3answers
47 views

How to find location of a point for a rectangle

I have a circle with a line that is drawn through it at two points. I have the coordinate for the center of the circle, the two coordinates where it intersects the circle and the radius as well. I ...
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1answer
44 views

Equation of a plane through intersection of two and parallel to other

I have got two planes $$x+y+z=1$$ and $$2x+3y-z+4=0$$ . I am required to find a plane by intersection of two and parallel to $x$ axis . I think the plane parallel to $x$ axis so Simply $P1+kP2=0$ ...
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1answer
86 views

Best way to plot a 4 dimensional meshgrid

I have $4$ variables $X$, $Y$, $Z$ and $C$, and I want to plot these on a graph. Usually I would just plot the surface $X$, $Y$, $Z$ and then use color to represent the $4$th dimension, as shown ...
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1answer
17 views

Proving the existence of a ____ number of conditions under a rotation of coordinates.

I'm reading a section on Rotation of Coordinate Systems and this is throwing me off: 'In n-dimensional space, the rotation matrix will have $n^2$ elements, upon which orthogonality relations place ...
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1answer
28 views

Coordinates of sector of circle

I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate ...
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1answer
28 views

Get yaw to point at X and Y values (2D)

I have $X$ and $Y$ coordinates. I also have another object. I need to figure out how set the yaw of the second object to point at the $X$ and $Y$ coordinates. How can I go about doing this?
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2answers
83 views

Let PQR be a right angled isosceles triangle right angled at P (2,1). If equation of line QR is $2x+y=3$, equations of PQ&PR

Let PQR be a right angled isosceles triangle right angled at P (2,1). If equation of line QR is $2x+y=3$, find combined equation of pair of lines PQ and PR.
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2answers
77 views

solving 3-d coordinates from x, y and z distance

I working with WiFi positioning and i want to know the exact coordinate where I am. Here is the problem..
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1answer
31 views

How to get coordinates of some area

I have a rectangle and I divide it into 8 triangle with same size. Top left corner is origin. I want to check that if a point is inside the black area or not. Lets say point's x coordinate is pointX ...
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2answers
112 views

What is (fundamentally) a coordinate system ?

Consider the following construction of vectors and points. Let's start with a vector space, or more specifically a coordinate space $F^N$ over a field $F$ and of $N$ dimensions. The elements of this ...
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3answers
80 views

Origin in vector space?

In the wikipedia article about vector space I do not understand this sentence Roughly, affine spaces are vector spaces whose origin is not specified. A vector space does not need an origin. When ...
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28 views

symplectic coordinate change in tangent space

Given is the Hamiltonian system with energy function $$H(q,p) = \sum_{i = 1}^{2} \frac{p_{i}^{2}}{2m_{i}} + m_{i}V(q_{i}) = H_{0},$$ where $H_{0}$ is some positive constant and the potential energy ...
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1answer
129 views

Rigorous definition and relations between point/vector/affine space/vector space/basis/frame/coordinate system

I am trying to understand the exact relation between all these things: point vector affine space vector space basis frame coordinate system Can you explain me rigorously (in the mathematical ...
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1answer
56 views

Locus of center of circle.

Consider two circles with radii $a$ and $b$ and centers $(a, 0)$ and $(b, 0)$ respectively with $0 < a < b$. Let $c$ be the center of any circle in the crescent shaped region M between the two ...
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1answer
90 views

What are the coordinates of the ends of the latus rectum of the parabola $x^2 - 2y + 2 = 0$? [duplicate]

I've already graphed the parabola . i just don't know how to locate it's focus and the ends of it's latus rectum. On my graph, the vertex is on (0,1). Please help me with this. ASAP.
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1answer
22 views

Determining object rotation

I have an 8x8 square(room) with an object in it at the coords of (0, 0). If I rotate that square clockwise once, that object is now at (0, 7). I do it again an it's at (7, 7), and once more it's at ...
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1answer
77 views

Calculate possible intersection point of two lines

I'd like to know the $I$ coordinates $[x, y]$. $I$ is the possible intersection point of line $|AB|$ with $|XY|$ and $|X'Y'|$. Values that are known: Angle $AIX$ and $AIX'$ Coordinates of points ...
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1answer
13 views

Position Value in a Triangle

I have a triangle. Each of the 3 corners is assigned a different value. Lets say corner 1 is 100, corner 2 is 200, and corner 3 is 300. I want to pick a coordinate in the middle of the triangle and ...
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1answer
27 views

Possible path of a fixed length formula

I am looking for a formula that gives me all possible combinations of getting from point A(ax,ay) to point B(bx,by) using a ...
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1answer
62 views

How do I calculate a point's coordinates on a circle’s circumference

I have got a circle with radius $r$ and center point $c_x$ and $c_y$. Known values: - $c_x$ and $c_y$ - $r$ - length $AR_a$ - length $BR_b$ Angle between point $A$ and the radius $r$ is unknown ...
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1answer
29 views

A coordinate geometry question.

On pg. 46 of "Coordinate geometry" by S.L. Loney, the following question has been posed: Show that the equations to the straight lines passing through the point $(3,-2)$ and inclined at $60^\circ$ ...
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34 views

Looking for certain functions or a coordinate transform respectively

I want to generate an image of the mandelbrot set. That means to map the x-y-coordinate-system, where the mandelbrot set lives (e.g. x:-2 .. 1; y:-1.5 .. 1.5) to an screen coordinate-system u-v (say ...
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0answers
78 views

Change of basis matrix notation confusion

I've got strange notation of change of basis matrix in my book and I'd like to have it explained a little bit. It says, if: $M _{\mathcal A}^{\mathcal B}(id) \cdot \vec{v} _{\mathcal B} = ...
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1answer
91 views

Finding the coordinates of a point in a given rectangle

I'm working on a computer program that displays on a screen that is 1280x800 pixels. I have a point that exists within the coordinates of the screen at the middle/origin. That gives me a view of 400 ...
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1answer
27 views

A rectangle $OACB$ with two axes as two sides,the origin $O$ as a vertex is drawn in which the length $OA$ is four times the width $OB$…

A rectangle $OACB$ with two axes as two sides,the origin $O$ as a vertex is drawn in which the length $OA$ is four times the width $OB$.A circle is drawn passing through the points BC and touching ...
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1answer
31 views

Deriving Cartesian Coordinates from Cylindrical Coordinates

The ans given was: $x = r \cos (\alpha)$ $y = h$ $z = -r \sin(\alpha)$ Could somebody explain to me how to arrive at the formula? I'm probably confused with the axes because usually, the $Z$ ...
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0answers
153 views

Reverse rotation back to original coordinates (Euler Angles)

so in the program I'm trying to write (still, it's a mathematical question) I have a set of coordinates and angles (Euler angles) which represent the place and orientation of an object in space, ...
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1answer
23 views

Determining whether a 3-dimensional equations creates a horizontal or non-horizontal plane?

I am learning about graphing 3-dimensional shapes on x,y,z coordinates axis and am understanding everything for the most part. However, the thing that is continuously tripping me up is distinguishing ...
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2answers
42 views

Coordinates rotation by $120$ degree

If I have a point on a standard grid with coordinates say: $A_1=(1000,0)$ $A_2=(707,707)$ Is there a easy way to transfer this points to $\pm 120$ degrees from the origin $(0,0)$, and ...
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1answer
70 views

How to calculate the points of the triangles making up an Octahedron?

Ok guys, I'm not a great mathematician but will try to work this as accurately as I can. I hope someone can help me. I am drawing some 3D objects and I am having trouble drawing an Octahedron. I ...
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43 views

Derivative in non orthogonal coordinates

I am trying to transform irregular shape in common Cartesian coordinates ($x-y$) into a regular shape in a generalized coordinates(e.g.,$u-v$), in which the transform can be defined as $u=u(x,y)$ and ...