# Tagged Questions

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### 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 $1-t$, $2t$.
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### 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 ...
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### How to find a 2D basis within a 3D plane - direct matrix method?

I have a plane equation in 3D, in the form $Ax+By+Cz+D=0$ (or equivalently, $\textbf{x}\cdot\textbf{n} = \textbf{a}\cdot\textbf{n}$), where $\textbf{n}=\left[A\:B\:C\right]^T$ is the plane normal, and ...
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### 2D Cartesian Matrix / coordinate transformation.

I has initially asked this question in the programming site but did not get an answer that worked. This is my first question on this site so please bear with me. Consider a page with three distinct ...
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### Jacobian matrix normalization

I have a problem with normalization of the Jacobian matrix. There seems to be no clear method for doing it: in some literature, it has been normalized by using some characteristic length, which is ...
### How to find the $P_2$ when $T_1P_1=T_2P_2$
$T_1$ and $T_2$ are $3 \times 3$ homogenous transform matrices. $P_1$ is the $3 \times 1$ matrix with $x, y$ coordinates of point $P_1$. What I am trying to do here is trying to get $x, y$ coordinate ...