I have three points $A(x,y) , B(x,y)$ and $C(x,y)$ the $x$ and $y$ coordinates follow a normal distribution with a known mean and variance. I don,t know if $A$ and $B$ are correlated with each other. I know $C$ dont have an correlation with $A$ and $B$.
There is a line made bij $AB$ and the point $C$. i want to calculate the distance from $C$ to the line $AB$. that means there is an orthogonal line from $C$ on $AB$. the length of that line is calculed with the next formule : $det(A)/|a-b|$ $A$ is an matrix made bij $(a-c,a-b)$
Atm i am using a monte carlo simulation to find the variance and mean. with the simulation, i found that the distance follow a normal distribution. Anyone can help me out? Is it possible to calculate the variance of the length of the orthogonal line without the use of a simulation?
I am not allowed to upload the plot of the points. the dataframe of the points excist of 4096 points located on the map. i have to find for each point a line with the smallest distence. the points are from an other map. the company want to combine those maps to create an better map