updated pictureI am trying to find the formula or at least the name of this operation to locate x and y coordinates for a point from two other reference points with x and y known and distance to third point known as well. the distance between the two static point and the unknown third point will change. so i need a formula to locate the third point based off those distances. Thank you for any help you can give.
here is an updated pic with the mappings
Assume A is (0,0), B is (4,0) in your picture, and C is the point you need to know. And AD $\bot$ AB, with D on AB. So that $$AC^2=(AD^2+CD^2), BC^2=((AB-AD)^2+CD^2)$$ let $AB=a,AC=b,BC=c$, in your case $a=4,b=3,c=2$. The above is $$b^2-AD^2=c^2-(a-AD)^2$$ which can solve $AD$ which is the x coordinate of $C$. The result is $$AD=\frac{a^2+b^2-c^2}{2a}$$ Then bring it back to find $$CD=\pm\sqrt{b^2-(\frac{a^2+b^2-c^2}{2a})^2}$$, and $CD$ is the y coordinate of $C$, so $$C=(\frac{a^2+b^2-c^2}{2a},\pm\sqrt{b^2-(\frac{a^2+b^2-c^2}{2a})^2})=(\frac{21}{8},\pm \sqrt{\frac{51}{8}})$$Hope it can help