Question

One side of a square is inclined to the x-axis at an angle and one of the extremities is at the origin. If the side of square is 4 find the equation of the diagonals of the square.

Answer 1

Let 

We have the vertices: 

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Diagonal  has points 
. . . and we can write its equation: 



 **

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Diagonal  has [point 
. . . and we can write its equation: 







~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

** This can be simplified, if desired.