Perl 6, 44 bytes
{!im ($^b-$^a)*($^d-$^c)/(($d-$a)*($b-$c)):}
Takes vertices as complex numbers. Uses the fact that the sum of opposite angles is 180° in a cyclic quadrilateral. The order of operations should guarantee that floating-point operations yield an exact result for (small enough) integers.
Port of Misha Lavrov's TI-Basic solution, 33 bytes
{).im}
Perl 6, 44 bytes
{!im ($^b-$^a)*($^d-$^c)/(($d-$a)*($b-$c)):}
Takes vertices as complex numbers. Uses the fact that the sum of opposite angles is 180° in a cyclic quadrilateral. The order of operations should guarantee that floating-point operations yield an exact result for (small enough) integers.
Perl 6, 44 bytes
{!im ($^b-$^a)*($^d-$^c)/(($d-$a)*($b-$c)):}
Takes vertices as complex numbers. Uses the fact that the sum of opposite angles is 180° in a cyclic quadrilateral. The order of operations should guarantee that floating-point operations yield an exact result for (small enough) integers.
Port of Misha Lavrov's TI-Basic solution, 33 bytes
{).im}
Perl 6, 44 bytes
{!im ($^c$^b-$^a)*($^b-$^d-$^c)/(($b$d-$a)*($c$b-$d$c)):}
Takes vertices as complex numbers. Uses the fact that the sum of opposite angles is 180° in a cyclic quadrilateral. The order of operations should guarantee that floating-point operations yield an exact result for (small enough) integers.
Perl 6, 44 bytes
{!im ($^c-$^a)*($^b-$^d)/(($b-$a)*($c-$d)):}
Takes vertices as complex numbers. Uses the fact that the sum of opposite angles is 180° in a cyclic quadrilateral. The order of operations should guarantee that floating-point operations yield an exact result for (small enough) integers.
Perl 6, 44 bytes
{!im ($^b-$^a)*($^d-$^c)/(($d-$a)*($b-$c)):}
Takes vertices as complex numbers. Uses the fact that the sum of opposite angles is 180° in a cyclic quadrilateral. The order of operations should guarantee that floating-point operations yield an exact result for (small enough) integers.
Perl 6, 44 bytes
{!im ($^c-$^a)*($^b-$^d)/(($b-$a)*($c-$d)):}
Takes vertices as complex numbers. Uses the fact that the sum of opposite angles is 180° in a cyclic quadrilateral. The order of operations should guarantee that floating-point operations yield an exact result for (small enough) integers.