[Math] Calculate the unknown coordinates of a point $B (x_2,y_2)$ on a line with given distance from a known point $A(x_1,y_1)$

geometrylinear algebra

I have a line which represents a cross section. I have the coordinates of on its starting point. I need the coordinates of the end point of that cross section line. The distance between these two points is known. Is there some way to calculate it, or do I need some more information?

I want to calculate the unknown coordinates of end point $B (x_2,y_2)$ on a line with given distance from a known coordinates of starting point $A(x_1,x_2)$.

Clarification

I have a cross section line AB with length of $2800$m. The start point $A(x_1,y_1,z_1)$ is known. $z_1$ is the bed elevation on point $A$. I need to calculate the coordinates at end point $B(x_2,y_2)$. Now there are two situations.

  • Case 1: I have $z_2$ at point $B$ with me also.
  • Case 2: I don't have $z_2$ on point $B$ with me.

Best Answer

Assuming no typo in what you wrote and that I properly understood (this does not seem to be sure according to the comments I received after my initial answer), if you have point $A$ $(x_1,x_2)$ and point $B$ $(x_2,y_2)$ the square of the distance is given by $$d^2=(x_1-x_2)^2+(x_2-y_2)^2$$

I am sure that you can take from here.

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