Calculate x2 if we know distance, x1, y1, y2

Question

How can I calculate x1 in Java if I know the distance, x2, y1 and y2 of two points.

I made a picture to be easier to understand:

If we know the x1, x2, y1, y2 is easy to calculate the distance. But if we know the distance? How can I calculate with delta?

Answer 1

Note that there are usually two solutions to this; corresponding to essentially what is a 'reflected' solution.

if d is the distance, then x2 is at

x1 +/- sqrt(d * d - (y2 - y1) * (y2 - y1));

Where +/- means "plus or minus". That is to repeat, x1 can be in two different places.

Answer 2

d^2 = (x2-x1)^2 + (y2-y1)^2

(x2-x1)^2 = d^2 - (y2-y1)^2

x2-x1 = +- sqrt(d^2 - (y2-y1)^2)

x2 = x1 +- sqrt(d^2 - (y2-y1)^2)

Answer 3

If you know the distance, you can use it's formula:

d = sqrt(sqr(x2 - x1) + sqr(y2 - y1))

With that, you can re-arrange it to find x1 using simple algebra, but I'll let you figure that out.

Answer 4

First, you need to solve for x2:

d = sqrt((x1-x2)^2+(y1-y2)^2)
d^2 = (x1-x2)^2+(y1-y2)^2
d^2-(y1-y2)^2 = (x1-x2)^2
sqrt(d^2-(y1-y2)^2) = (x1-x2)
x2 = x1-sqrt(d^2-(y1-y2)^2)

Now, it's just a matter of expressing this in java:

double x2 = x1 - Math.sqrt(Math.pow(d, 2) - Math.pow(y1 - y2, 2));