#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/4/CGL/1/CGL_1_A"
#define ERROR 1e-8
#include "../../cpp/template/template.cpp"
#include "../../cpp/geometry/projection.cpp"
int main(){
Point p1,p2;cin>>p1>>p2;
Line l(p1, p2);
int q;cin>>q;
for(int i = 0; q > i; i++){
Point q;cin>>q;
cout << fixed << setprecision(10) << projection(l,q) << endl;
}
}
#line 1 "cpp/z_test/aoj-CGL_1_A.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/4/CGL/1/CGL_1_A"
#define ERROR 1e-8
#line 2 "cpp/template/template.cpp"
//yukicoder@cpp17
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <cctype>
#include <climits>
#include <cassert>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <random>
#include <bitset>
#include <complex>
#include <utility>
#include <numeric>
#include <functional>
using namespace std;
using ll = long long;
using P = pair<ll,ll>;
const ll MOD = 998244353;
const ll MODx = 1000000007;
const int INF = (1<<30)-1;
const ll LINF = (1LL<<62LL)-1;
const double EPS = (1e-10);
P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}};
P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}};
template <typename T> vector<T> make_vector(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_vector(size_t a, Ts... ts) { return vector<decltype(make_vector(ts...))>(a, make_vector(ts...)); }
/*
確認ポイント
cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる
計算量は変わらないが楽できるシリーズ
min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる
count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる
*/
/* comment outed because can cause bugs
__attribute__((constructor))
void initial() {
cin.tie(0);
ios::sync_with_stdio(false);
}
*/
#line 5 "cpp/z_test/aoj-CGL_1_A.test.cpp"
#line 2 "cpp/geometry/vec.hpp"
struct Vec{
long double x,y;
Vec operator*(long double a){
return {x*a, y*a};
}
Vec operator/(long double a){
return {x/a, y/a};
}
friend ostream &operator<<(ostream &os, const Vec &p){
return os << p.x << " " << p.y;
}
};
long double magnitude(Vec v){
return sqrt(v.x*v.x+v.y*v.y);
}
Vec standardize(Vec v){
return v/magnitude(v);
}
#line 3 "cpp/geometry/point.hpp"
struct Point{
long double x,y;
Vec operator-(Point b){
return {x-b.x, y-b.y};
}
Point operator+(long double a){
return {x+a, y+a};
}
Point operator+(Vec v){
return {x+v.x, y+v.y};
}
friend istream &operator>>(istream &is, Point &p){
long double a,b;
cin>>a>>b;
p = Point({a,b});
return (is);
}
friend ostream &operator<<(ostream &os, const Point &p){
return os << p.x << " " << p.y;
}
};
#line 2 "cpp/geometry/line-segment.hpp"
#line 4 "cpp/geometry/line-segment.hpp"
struct LineSegment{
Point first, second;
LineSegment(Point a, Point b):first(a),second(b){}
};
#line 5 "cpp/geometry/linevec.hpp"
struct LineVec{
Point base;
Vec vec;
LineVec(LineSegment ls){
base = ls.first;
vec = ls.second - ls.first;
}
};
#line 5 "cpp/geometry/line.hpp"
struct Line{
//ax+by+c=0 (required: a*a+b*b != 0)
long double a,b,c;
Line(long double a, long double b, long double c): a(a), b(b), c(c){}
Line(LineVec lv){
a = -lv.vec.y;
b = lv.vec.x;
c = -(a*lv.base.x + b*lv.base.y);
}
Line operator/(long double v){
return {a/v, b/v, c/v};
}
Line(LineSegment ls){
(*this) = (LineVec)(ls);
}
Line(Point a, Point b){
LineSegment ls({a,b});
(*this) = (LineSegment)(ls);
}
};
Line standardize(Line l){
return l/sqrt(l.a*l.a+l.b*l.b);
}
long double distance(Line l, Point p){
Line nl = standardize(l);
return nl.a*p.x + nl.b*p.y + nl.c;
}
Vec normal(Line l){
Vec v = {-l.a, -l.b};
return standardize(v);
}
#line 5 "cpp/geometry/projection.cpp"
long double projectionDistance(Line l, Point p){
Line nl = standardize(l);
return distance(l, p);
}
Point projection(Line l, Point p){
long double dist = projectionDistance(l, p);
Vec v = normal(l);
return p+(v*dist);
}
#line 7 "cpp/z_test/aoj-CGL_1_A.test.cpp"
int main(){
Point p1,p2;cin>>p1>>p2;
Line l(p1, p2);
int q;cin>>q;
for(int i = 0; q > i; i++){
Point q;cin>>q;
cout << fixed << setprecision(10) << projection(l,q) << endl;
}
}
cpp/z_test/aoj-CGL_1_A.test.cpp
cpp/geometry/two-points-distance.cpp