Let the opposite angular points of a square be `(3,4)a n d(1,-1)` . Find the coordinates of the remaining angular points.

Explanation

Let `A B C D` be a square and let `A(3,4)` and `C(1,-1)` be the given angular points.


Let `B(x, y)` be the unknown vertex.


Then, `A B=B C`



`Rightarrow quad {AB}^{2}={BC}^{2} `


`Rightarrow quad({x}-3)^{2}+({y}-4)^{2}=({x}-1)^{2}+({y}+1)^{2}`


`Rightarrow quad 4 {x}+10 {y}-23=0 `


`Rightarrow quad {x}=frac{23-10 {y}}{4}`


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