# Find Corners of Rectangle using mid points

Consider a rectangle ABCD, we’re given the co-ordinates of the mid points of side AD and BC (p and q respectively) along with their length L (AD = BC = L). Now given the parameters, we need to print the co-ordinates of the 4 points A, B, C and D.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend **live classes **with experts, please refer **DSA Live Classes for Working Professionals **and **Competitive Programming Live for Students**.

Examples:

Input : p = (1, 0) q = (1, 2) L = 2 Output : (0, 0), (0, 2), (2, 2), (2, 0) Explanation: The printed points form a rectangle which satisfy the input constraints. Input : p = (1, 1) q = (-1, -1) L = 2*sqrt(2) Output : (0, 2), (-2, 0), (0, -2), (2, 0)

From the problem statement 3 cases can arise :

- The Rectangle is horizontal i.e., AD and BC are parallel to X-axis
- The Rectangle is vertical i.e., AD and BC are parallel to Y-axis
- The Rectangle is inclined at a certain angle with the axes

The first two cases are trivial and can easily be solved using basic geometry. For the third case we need to apply some mathematical concepts to find the points.

Consider the above diagram for clarity. We have the co-ordinates of p and q. Thus we can find the slope of AD and BC (As pq is perpendicular to AD). Once we have the slope of AD, we can find the equation of straight line passing through AD. Now we can apply distance formula to obtain the displacements along X and Y axes.

If slope of AD = m, then m = (p.x- q.x)/(q.y - p.y) and displacement along X axis, dx = L/(2*sqrt(1+m*m)) Similarly, dy = m*L/(2*sqrt(1+m*m))

Now we can simply find the co-ordinates of 4 corners by simply adding and subtracting the displacements obtained accordingly.

Below is the implementation .

## C++

`// C++ program to find corner points of` `// a rectangle using given length and middle` `// points.` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Structure to represent a co-ordinate point` `struct` `Point` `{` ` ` `float` `x, y;` ` ` `Point()` ` ` `{` ` ` `x = y = 0;` ` ` `}` ` ` `Point(` `float` `a, ` `float` `b)` ` ` `{` ` ` `x = a, y = b;` ` ` `}` `};` `// This function receives two points and length` `// of the side of rectangle and prints the 4` `// corner points of the rectangle` `void` `printCorners(Point p, Point q, ` `float` `l)` `{` ` ` `Point a, b, c, d;` ` ` `// horizontal rectangle` ` ` `if` `(p.x == q.x)` ` ` `{` ` ` `a.x = p.x - (l/2.0);` ` ` `a.y = p.y;` ` ` `d.x = p.x + (l/2.0);` ` ` `d.y = p.y;` ` ` `b.x = q.x - (l/2.0);` ` ` `b.y = q.y;` ` ` `c.x = q.x + (l/2.0);` ` ` `c.y = q.y;` ` ` `}` ` ` `// vertical rectangle` ` ` `else` `if` `(p.y == q.y)` ` ` `{` ` ` `a.y = p.y - (l/2.0);` ` ` `a.x = p.x;` ` ` `d.y = p.y + (l/2.0);` ` ` `d.x = p.x;` ` ` `b.y = q.y - (l/2.0);` ` ` `b.x = q.x;` ` ` `c.y = q.y + (l/2.0);` ` ` `c.x = q.x;` ` ` `}` ` ` `// slanted rectangle` ` ` `else` ` ` `{` ` ` `// calculate slope of the side` ` ` `float` `m = (p.x-q.x)/` `float` `(q.y-p.y);` ` ` `// calculate displacements along axes` ` ` `float` `dx = (l /` `sqrt` `(1+(m*m))) *0.5 ;` ` ` `float` `dy = m*dx;` ` ` `a.x = p.x - dx;` ` ` `a.y = p.y - dy;` ` ` `d.x = p.x + dx;` ` ` `d.y = p.y + dy;` ` ` `b.x = q.x - dx;` ` ` `b.y = q.y - dy;` ` ` `c.x = q.x + dx;` ` ` `c.y = q.y + dy;` ` ` `}` ` ` `cout << a.x << ` `", "` `<< a.y << ` `" n"` ` ` `<< b.x << ` `", "` `<< b.y << ` `"n"` `;` ` ` `<< c.x << ` `", "` `<< c.y << ` `" n"` ` ` `<< d.x << ` `", "` `<< d.y << ` `"nn"` `;` `}` `// Driver code` `int` `main()` `{` ` ` `Point p1(1, 0), q1(1, 2);` ` ` `printCorners(p1, q1, 2);` ` ` `Point p(1, 1), q(-1, -1);` ` ` `printCorners(p, q, 2*` `sqrt` `(2));` ` ` `return` `0;` `}` |

## Java

`// Java program to find corner points of` `// a rectangle using given length and middle` `// points.` `class` `GFG` `{` ` ` `// Structure to represent a co-ordinate point` ` ` `static` `class` `Point` ` ` `{` ` ` `float` `x, y;` ` ` `Point()` ` ` `{` ` ` `x = y = ` `0` `;` ` ` `}` ` ` `Point(` `float` `a, ` `float` `b)` ` ` `{` ` ` `x = a;` ` ` `y = b;` ` ` `}` ` ` `};` ` ` `// This function receives two points and length` ` ` `// of the side of rectangle and prints the 4` ` ` `// corner points of the rectangle` ` ` `static` `void` `printCorners(Point p, Point q, ` `float` `l)` ` ` `{` ` ` `Point a = ` `new` `Point(), b = ` `new` `Point(),` ` ` `c = ` `new` `Point(), d = ` `new` `Point();` ` ` `// horizontal rectangle` ` ` `if` `(p.x == q.x)` ` ` `{` ` ` `a.x = (` `float` `) (p.x - (l / ` `2.0` `));` ` ` `a.y = p.y;` ` ` `d.x = (` `float` `) (p.x + (l / ` `2.0` `));` ` ` `d.y = p.y;` ` ` `b.x = (` `float` `) (q.x - (l / ` `2.0` `));` ` ` `b.y = q.y;` ` ` `c.x = (` `float` `) (q.x + (l / ` `2.0` `));` ` ` `c.y = q.y;` ` ` `}` ` ` `// vertical rectangle` ` ` `else` `if` `(p.y == q.y)` ` ` `{` ` ` `a.y = (` `float` `) (p.y - (l / ` `2.0` `));` ` ` `a.x = p.x;` ` ` `d.y = (` `float` `) (p.y + (l / ` `2.0` `));` ` ` `d.x = p.x;` ` ` `b.y = (` `float` `) (q.y - (l / ` `2.0` `));` ` ` `b.x = q.x;` ` ` `c.y = (` `float` `) (q.y + (l / ` `2.0` `));` ` ` `c.x = q.x;` ` ` `}` ` ` `// slanted rectangle` ` ` `else` ` ` `{` ` ` `// calculate slope of the side` ` ` `float` `m = (p.x - q.x) / (q.y - p.y);` ` ` `// calculate displacements along axes` ` ` `float` `dx = (` `float` `) ((l / Math.sqrt(` `1` `+ (m * m))) * ` `0.5` `);` ` ` `float` `dy = m * dx;` ` ` `a.x = p.x - dx;` ` ` `a.y = p.y - dy;` ` ` `d.x = p.x + dx;` ` ` `d.y = p.y + dy;` ` ` `b.x = q.x - dx;` ` ` `b.y = q.y - dy;` ` ` `c.x = q.x + dx;` ` ` `c.y = q.y + dy;` ` ` `}` ` ` `System.out.print((` `int` `)a.x + ` `", "` `+ (` `int` `)a.y + ` `" \n"` ` ` `+ (` `int` `)b.x + ` `", "` `+ (` `int` `)b.y + ` `"\n"` ` ` `+ (` `int` `)c.x + ` `", "` `+ (` `int` `)c.y + ` `" \n"` ` ` `+ (` `int` `)d.x + ` `", "` `+ (` `int` `)d.y + ` `"\n"` `);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `Point p1 = ` `new` `Point(` `1` `, ` `0` `), q1 = ` `new` `Point(` `1` `, ` `2` `);` ` ` `printCorners(p1, q1, ` `2` `);` ` ` `Point p = ` `new` `Point(` `1` `, ` `1` `), q = ` `new` `Point(-` `1` `, -` `1` `);` ` ` `printCorners(p, q, (` `float` `) (` `2` `* Math.sqrt(` `2` `)));` ` ` `}` `}` `// This code contributed by Rajput-Ji` |

## Python3

`# Python3 program to find corner points of` `# a rectangle using given length and middle` `# points.` `import` `math` `# Structure to represent a co-ordinate point` `class` `Point:` ` ` ` ` `def` `__init__(` `self` `, a ` `=` `0` `, b ` `=` `0` `):` ` ` ` ` `self` `.x ` `=` `a` ` ` `self` `.y ` `=` `b` ` ` `# This function receives two points and length` `# of the side of rectangle and prints the 4` `# corner points of the rectangle` `def` `printCorners(p, q, l):` ` ` ` ` `a, b, c, d ` `=` `Point(), Point(), Point(), Point()` ` ` ` ` `# Horizontal rectangle` ` ` `if` `(p.x ` `=` `=` `q.x):` ` ` `a.x ` `=` `p.x ` `-` `(l ` `/` `2.0` `)` ` ` `a.y ` `=` `p.y` ` ` ` ` `d.x ` `=` `p.x ` `+` `(l ` `/` `2.0` `)` ` ` `d.y ` `=` `p.y` ` ` ` ` `b.x ` `=` `q.x ` `-` `(l ` `/` `2.0` `)` ` ` `b.y ` `=` `q.y` ` ` ` ` `c.x ` `=` `q.x ` `+` `(l ` `/` `2.0` `)` ` ` `c.y ` `=` `q.y` ` ` ` ` `# Vertical rectangle` ` ` `elif` `(p.y ` `=` `=` `q.y):` ` ` `a.y ` `=` `p.y ` `-` `(l ` `/` `2.0` `)` ` ` `a.x ` `=` `p.x` ` ` ` ` `d.y ` `=` `p.y ` `+` `(l ` `/` `2.0` `)` ` ` `d.x ` `=` `p.x` ` ` ` ` `b.y ` `=` `q.y ` `-` `(l ` `/` `2.0` `)` ` ` `b.x ` `=` `q.x` ` ` ` ` `c.y ` `=` `q.y ` `+` `(l ` `/` `2.0` `)` ` ` `c.x ` `=` `q.x` ` ` ` ` `# Slanted rectangle` ` ` `else` `:` ` ` ` ` `# Calculate slope of the side` ` ` `m ` `=` `(p.x ` `-` `q.x) ` `/` `(q.y ` `-` `p.y)` ` ` ` ` `# Calculate displacements along axes` ` ` `dx ` `=` `(l ` `/` `math.sqrt(` `1` `+` `(m ` `*` `m))) ` `*` `0.5` ` ` `dy ` `=` `m ` `*` `dx` ` ` ` ` `a.x ` `=` `p.x ` `-` `dx` ` ` `a.y ` `=` `p.y ` `-` `dy` ` ` ` ` `d.x ` `=` `p.x ` `+` `dx` ` ` `d.y ` `=` `p.y ` `+` `dy` ` ` ` ` `b.x ` `=` `q.x ` `-` `dx` ` ` `b.y ` `=` `q.y ` `-` `dy` ` ` ` ` `c.x ` `=` `q.x ` `+` `dx` ` ` `c.y ` `=` `q.y ` `+` `dy` ` ` ` ` `print` `(` `int` `(a.x), ` `", "` `, ` `int` `(a.y), sep ` `=` `"")` ` ` `print` `(` `int` `(b.x), ` `", "` `, ` `int` `(b.y), sep ` `=` `"")` ` ` `print` `(` `int` `(c.x), ` `", "` `, ` `int` `(c.y), sep ` `=` `"")` ` ` `print` `(` `int` `(d.x), ` `", "` `, ` `int` `(d.y), sep ` `=` `"")` ` ` `print` `()` ` ` `# Driver code` `p1 ` `=` `Point(` `1` `, ` `0` `)` `q1 ` `=` `Point(` `1` `, ` `2` `)` `printCorners(p1, q1, ` `2` `)` `p ` `=` `Point(` `1` `, ` `1` `)` `q ` `=` `Point(` `-` `1` `, ` `-` `1` `)` `printCorners(p, q, ` `2` `*` `math.sqrt(` `2` `))` `# This code is contributed by shubhamsingh10` |

## C#

`// C# program to find corner points of` `// a rectangle using given length and middle` `// points.` `using` `System;` `class` `GFG` `{` ` ` `// Structure to represent a co-ordinate point` ` ` `public` `class` `Point` ` ` `{` ` ` `public` `float` `x, y;` ` ` `public` `Point()` ` ` `{` ` ` `x = y = 0;` ` ` `}` ` ` `public` `Point(` `float` `a, ` `float` `b)` ` ` `{` ` ` `x = a;` ` ` `y = b;` ` ` `}` ` ` `};` ` ` `// This function receives two points and length` ` ` `// of the side of rectangle and prints the 4` ` ` `// corner points of the rectangle` ` ` `static` `void` `printCorners(Point p, Point q, ` `float` `l)` ` ` `{` ` ` `Point a = ` `new` `Point(), b = ` `new` `Point(),` ` ` `c = ` `new` `Point(), d = ` `new` `Point();` ` ` `// horizontal rectangle` ` ` `if` `(p.x == q.x)` ` ` `{` ` ` `a.x = (` `float` `) (p.x - (l / 2.0));` ` ` `a.y = p.y;` ` ` `d.x = (` `float` `) (p.x + (l / 2.0));` ` ` `d.y = p.y;` ` ` `b.x = (` `float` `) (q.x - (l / 2.0));` ` ` `b.y = q.y;` ` ` `c.x = (` `float` `) (q.x + (l / 2.0));` ` ` `c.y = q.y;` ` ` `}` ` ` ` ` `// vertical rectangle` ` ` `else` `if` `(p.y == q.y)` ` ` `{` ` ` `a.y = (` `float` `) (p.y - (l / 2.0));` ` ` `a.x = p.x;` ` ` `d.y = (` `float` `) (p.y + (l / 2.0));` ` ` `d.x = p.x;` ` ` `b.y = (` `float` `) (q.y - (l / 2.0));` ` ` `b.x = q.x;` ` ` `c.y = (` `float` `) (q.y + (l / 2.0));` ` ` `c.x = q.x;` ` ` `}` ` ` ` ` `// slanted rectangle` ` ` `else` ` ` `{` ` ` `// calculate slope of the side` ` ` `float` `m = (p.x - q.x) / (q.y - p.y);` ` ` `// calculate displacements along axes` ` ` `float` `dx = (` `float` `) ((l / Math.Sqrt(1 + (m * m))) * 0.5);` ` ` `float` `dy = m * dx;` ` ` `a.x = p.x - dx;` ` ` `a.y = p.y - dy;` ` ` `d.x = p.x + dx;` ` ` `d.y = p.y + dy;` ` ` `b.x = q.x - dx;` ` ` `b.y = q.y - dy;` ` ` `c.x = q.x + dx;` ` ` `c.y = q.y + dy;` ` ` `}` ` ` `Console.Write((` `int` `)a.x + ` `", "` `+ (` `int` `)a.y + ` `" \n"` ` ` `+ (` `int` `)b.x + ` `", "` `+ (` `int` `)b.y + ` `"\n"` ` ` `+ (` `int` `)c.x + ` `", "` `+ (` `int` `)c.y + ` `" \n"` ` ` `+ (` `int` `)d.x + ` `", "` `+ (` `int` `)d.y + ` `"\n"` `);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `Point p1 = ` `new` `Point(1, 0), q1 = ` `new` `Point(1, 2);` ` ` `printCorners(p1, q1, 2);` ` ` `Point p = ` `new` `Point(1, 1), q = ` `new` `Point(-1, -1);` ` ` `printCorners(p, q, (` `float` `) (2 * Math.Sqrt(2)));` ` ` `}` `}` `// This code has been contributed by 29AjayKumar` |

## Javascript

`<script>` `// Javascript program to find corner points of` `// a rectangle using given length and middle` `// points.` `// Structure to represent a co-ordinate point` `class Point` `{` ` ` `constructor(a,b)` ` ` `{` ` ` `this` `.x=a;` ` ` `this` `.y=b;` ` ` `}` `}` `// This function receives two points and length` ` ` `// of the side of rectangle and prints the 4` ` ` `// corner points of the rectangle` `function` `printCorners(p,q,l)` `{` ` ` `let a = ` `new` `Point(), b = ` `new` `Point(),` ` ` `c = ` `new` `Point(), d = ` `new` `Point();` ` ` ` ` `// horizontal rectangle` ` ` `if` `(p.x == q.x)` ` ` `{` ` ` `a.x = (p.x - (l / 2.0));` ` ` `a.y = p.y;` ` ` ` ` `d.x = (p.x + (l / 2.0));` ` ` `d.y = p.y;` ` ` ` ` `b.x = (q.x - (l / 2.0));` ` ` `b.y = q.y;` ` ` ` ` `c.x = (q.x + (l / 2.0));` ` ` `c.y = q.y;` ` ` `}` ` ` `// vertical rectangle` ` ` `else` `if` `(p.y == q.y)` ` ` `{` ` ` `a.y = (p.y - (l / 2.0));` ` ` `a.x = p.x;` ` ` ` ` `d.y = (p.y + (l / 2.0));` ` ` `d.x = p.x;` ` ` ` ` `b.y = (q.y - (l / 2.0));` ` ` `b.x = q.x;` ` ` ` ` `c.y = (q.y + (l / 2.0));` ` ` `c.x = q.x;` ` ` `}` ` ` `// slanted rectangle` ` ` `else` ` ` `{` ` ` `// calculate slope of the side` ` ` `let m = (p.x - q.x) / (q.y - p.y);` ` ` ` ` `// calculate displacements along axes` ` ` `let dx = ((l / Math.sqrt(1 + (m * m))) * 0.5);` ` ` `let dy = m * dx;` ` ` ` ` `a.x = p.x - dx;` ` ` `a.y = p.y - dy;` ` ` ` ` `d.x = p.x + dx;` ` ` `d.y = p.y + dy;` ` ` ` ` `b.x = q.x - dx;` ` ` `b.y = q.y - dy;` ` ` ` ` `c.x = q.x + dx;` ` ` `c.y = q.y + dy;` ` ` `}` ` ` ` ` `document.write(a.x + ` `", "` `+ a.y + ` `" <br>"` ` ` `+ b.x + ` `", "` `+ b.y + ` `"<br>"` ` ` `+ c.x + ` `", "` `+ c.y + ` `" <br>"` ` ` `+ d.x + ` `", "` `+ d.y + ` `"<br>"` `);` `}` `// Driver code` `let p1 = ` `new` `Point(1, 0), q1 = ` `new` `Point(1, 2);` `printCorners(p1, q1, 2);` `let p = ` `new` `Point(1, 1), q = ` `new` `Point(-1, -1);` `printCorners(p, q, (2 * Math.sqrt(2)));` `// This code is contributed by rag2127` `</script>` |

**Output:**

0, 0 0, 2 2, 2 2, 0 0, 2 -2, 0 0, -2 2, 0

**Reference:**

StackOverflow

This article is contributed by **Ashutosh Kumar** ðŸ˜€ If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.