let's say that I have two points. Points B and C. I know their coordinates. Point B is 2,3 and point C is 4,6. I also know that there is point A located on the line between B and C. I know that it is "height", it's y coordinate, and it is 4. How can I learn the x of point A?
It's important for me to find the easiest way to calculate that – I feel like I am missing something obvious. I found other question like that, but it involved point A being outside of line between B and C. In my case, my point is directly on the line between these two points.
Best Answer
With the given the information, the easiest way to determine $x_A$ is to equate the gradients of segments $BA$ and $BC$ (this is valid since $A,B,C$ are collinear): $$\frac{y_A-y_B}{x_A-x_B}=\frac{y_C-y_B}{x_C-x_B}\\\frac{y_A-y_B}{y_C-y_B}=\frac{x_A-x_B}{x_C-x_B}\\x_A=x_B+\frac{(x_C-x_B)(y_A-y_B)}{y_C-y_B}.$$