высоты

#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

struct vershina
{
  double x, y;
};

struct direct
{
 double k = 0, b = 0;
 double parametr = 0;
};

direct normal (direct one, vershina trig)
{
  direct normal;
  if (one.parametr == 0 && one.k != 0)
  {
    normal.k = -1/one.k;
    normal.b = trig.y - normal.k*trig.x;
  }
  else if (one.parametr != 0)
  {
    normal.k = 0;
    normal.b = trig.y;
  }
  else if (one.k == 0)
    normal.parametr = trig.x;
  //cout << normal.k << "x + " << normal.b << " " << normal.parametr << endl;
  return normal;
}

direct stright(vershina one, vershina two)
{
  direct stright;
  if(two.x - one.x != 0)
  {
    stright.k = (one.y - two.y)/(one.x - two.x);
    stright.b = one.y - stright.k*one.x;
  }
  else stright.parametr = one.x;
  return stright;
}

vershina otvet (direct normal_1, direct normal_2)
{
 vershina otvet;
 if (normal_1.parametr == 0 && normal_2.parametr == 0)
 {
   otvet.x = (normal_2.b - normal_1.b)/(normal_1.k - normal_2.k);
   otvet.y = normal_1.k*otvet.x + normal_1.b;
 }
 else if (normal_1.parametr != 0)
 {
   otvet.x = normal_1.parametr;
   otvet.y = normal_2.k*otvet.x + normal_2.b;
 }
 else if (normal_2.parametr != 0)
 {
   otvet.x = normal_2.parametr;
   otvet.y = normal_1.k*otvet.x + normal_1.b;
 }
 return otvet;
};

int main ()
{
  vershina A, B, C;
  cin >> A.x >> A.y >> B.x >> B.y >> C.x >> C.y;

  direct AB = stright(A, B);
  direct BC = stright(B, C);

  direct normal_one = normal(AB, C);
  direct normal_two = normal(BC, A);

  cout.precision(10);
  cout << fixed << otvet(normal_one, normal_two).x << " ";
  cout << fixed << otvet(normal_one, normal_two).y;
}