Question 773915
This can be done without using Distance Formula, since the four points are vertices of a square.  (You CAN use the distance formula if you want.)


Segment AD // segment CB
Line AD has slope {{{(0-(-3))/(4-0)=3/4}}}
Using point A(-3,1) and slope 3/4 in point-slope form equation,
{{{y-1=(3/4)(x-(-3))}}}
{{{y-1=(3/4)(x+3)}}}
{{{y=(3/4)(x+3)+1}}}
{{{y=(3/4)x+9/4+4/4}}}
Line AD______{{{highlight(y=(3/4)x+13/4)}}}


Segment BD // segment CA
Line BD has slope, since is perpendicular to line AD, of {{{-(4/3)}}}.
Using point B(4,0) and slope -(4/3) in point-slope form equation,
{{{y-0=-(4/3)(x-4)}}}
Line BD_____{{{highlight(y=-(4/3)x+16/3)}}}


Point D(?,?) is the intersection of the two lines, {{{highlight(y=(3/4)x+13/4)}}} and {{{highlight(y=-(4/3)x+16/3)}}}.



------remaining process would be solve the system.
------easiest way would be clear the fractions and use the equations in standard form..