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I have seen similar questions before but there most of the part is that in general they start from origin.But here is my question.

Just in a plane you have to construct triangle at some random place.The values of (x1,y1) and (x2,y2) are known and the length of the 3 sides of the triangle is given. How to find a general formula which would give the value of x3 and y3 as such.

I tried using distance formula in my notes which is basically squared root of the difference between x and y,but it got all messy.

The other Herons formula but everything is kind of messed up my head now

chethanv77777
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  • Welcome to MSE. Please use MathJax to format math on this site. To begin with, enclose all math expressions (including numbers) in $ signs. For example, $x_1^2$ will give you $x_1^2$. You'll get a much better response if your posts are easy to read. – saulspatz Apr 08 '21 at 11:09
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    Do you realize that there are two possibilities for the third point? How would you solve the problem with a pair of compasses? – saulspatz Apr 08 '21 at 11:10
  • If you know how to do it when when of the vertices is at the origin, then you can translate all your vertices by $(-x_1,-y_1)$ so your first vertex is now at the origin, solve the problem, then translate back by $(x_1,y_1)$. – acernine Apr 08 '21 at 11:23

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