Let say I have this image,
(X1, Y1), (X2, Y2) and (X3, Y3) are known points. From point (X1, Y1), a line is dropped perpendicular to line (X2, Y2) and (X3, Y3). I need to calculate (Xn, Yn)
Let say I have this image,
(X1, Y1), (X2, Y2) and (X3, Y3) are known points. From point (X1, Y1), a line is dropped perpendicular to line (X2, Y2) and (X3, Y3). I need to calculate (Xn, Yn)
you can easily find the equation of line joining two points.Suppose, $(X_n,Y_n)$ is the point of perpendicular projection from $(X_1,Y_1)$.We have two variables $X_n,Y_n$,so we need two independent equations.Condition 1, product of slopes of given line and line joining $(X_1,Y_1)$ and $(X_n,Y_n)$ is -1(as they are perpendicular).Second Condition,point $(X_n,Y_n)$ lies on the given line, hence satisfies its equation.Solution of these two equations will give the required point $(X_n,Y_n)$.
Here's how you can find it. You can find the slope of the line $L$ containing the points $(x_2,y_2)$ and $(x_3,y_3)$: you can then find the slope of the line $M$ through $(x_1,y_1)$ and $(x_n,y_n)$ (since these lines are perpendicular). Now are in a position to find the equations of $L$ and $M$, and hence the point of intersection, namely $(x_n,y_n)$.