# Check if given four points form a Square

In a 2d plane, four points are given. This algorithm will check whether four points are forming a square or not.

Checking for a square we have to match these conditions −

• All four sides formed by given points are same.
• All two connecting sides are right-angled.

## Input and Output

Input:
Four points {(20, 10), (10, 20), (20, 20), (10, 10)}
Output:
Points are forming a square.

## Algorithm

isFormingSquare(p1, p2, p3, p4)

In this procedure, we will use a method squareDist(p1, p2), it will return squared distance of two given points.

Input: Four points.

Output: True when given points are forming a square.

Begin
dist12 := squareDist(p1, p2)
dist13 := squareDist(p1, p3)
dist14 := squareDist(p1, p4)

if dist12 = dist13 and 2*dist12 = dist14, then
dist := squareDist(p2, p4)
return true when dist = squareDist(p3, p4) and dist = dist12
if dist13 = dist14 and 2*dist13 = dist12, then
dist := squareDist(p2, p3)
return true when dist = squareDist(p2, p4) and dist = dist13
if dist12 = dist14 and 2*dist12 = dist13, then
dist := squareDist(p2, p3)
return true when dist = squareDist(p3, p4) and dist = dist12
return false
End

## Example

#include<iostream>
using namespace std;

struct Point {
int x, y;
};

int squareDist(Point p, Point q) {
return (p.x - q.x)*(p.x - q.x) + (p.y - q.y)*(p.y - q.y);
}

bool isSquare(Point p1, Point p2, Point p3, Point p4) {    //check four points are forming square or not
int dist12 = squareDist(p1, p2);     // distance from p1 to p2
int dist13 = squareDist(p1, p3);     // distance from p1 to p3
int dist14 = squareDist(p1, p4);     // distance from p1 to p4

//when length of p1-p2 and p1-p3 are same, and square of (p1-p4) = 2*(p1-p2)
if (dist12 == dist13 && 2*dist12 == dist14) {
int dist = squareDist(p2, p4);
return (dist == squareDist(p3, p4) && dist == dist12);
}

//same condition for all other combinations
if (dist13 == dist14 && 2*dist13 == dist12) {
int dist = squareDist(p2, p3);
return (dist == squareDist(p2, p4) && dist == dist13);
}

if (dist12 == dist14 && 2*dist12 == dist13) {
int dist = squareDist(p2, p3);
return (dist == squareDist(p3, p4) && dist == dist12);
}
return false;
}

int main() {
Point p1 = {20, 10}, p2 = {10, 20}, p3 = {20, 20}, p4 = {10, 10};
if(isSquare(p1, p2, p3, p4))
cout << "Points are forming a square.";
else
cout << "Points are not forming a square";
}

## Output

Points are forming a square. 