If two opposite vertices of a square are (1,2) and (5,8) find the coordinates of its other two vertices and the equations of its sides.

Explanation

Let
`A(1, 2)`, `C(5, 8)`, `B(x1,y1)`, `D(x2,y2)`


Slope of `AC =(8−2)/(5−1)=6/4=3/2`


Let m be the slope of a line making an angle `45∘` with AC.


`∴tan 45∘=∣(m1−3/2)/(1+m×3/2)∣`


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