How To Check if a Given Point Lies Inside a Rectangle in Java?

A Rectangle is a closed two-dimensional shape that has 4 sides and 4 corners. The opposite sides are of the same length and parallel to each other. All 4 interior angles are equal, angles measure 90 degrees. It is a four-sided polygon.

Following is the diagram of the Rectangle:

Checking Points Inside Rectangle

A point is said to lie inside a rectangle if its x and y coordinates are between the x and y coordinates of the opposite corners of the rectangle. To determine whether the point lies within the rectangle, we will use the following approaches:

• If bottom left corner and top right corner point values are given
• If four points of the rectangle are given

If bottom left corner and top right corner point values are given

Then the given point x coordinate should lie inside the x coordinates of the rectangle, and the given point y coordinate should lie inside the y coordinates of the rectangle.

If four points of the rectangle are given

Then find the area of the rectangle and check that it should be the same as the four triangle areas formed by the point.

Input & Output Scenarios

Below are a few input and output scenarios that help you to understand how to check whether the point lies inside the rectangle:

Scenario 1

Suppose the bottom left corner and top right corner point values are (1, 1) and (9, 8), respectively.

Input: points = (x1 = 1, y1 = 1), (x2 = 9, y2 = 8) and (x = 2, y = 3)
Output: Yes

Calculation: x > x1 and x < x2, y > y1 and y < y2

As you can see, the point x is greater than x1 but less than x2; similarly, the point y is greater than y1 but less than y2, and the point (2, 3) lies inside the rectangle.

Scenario 2

Suppose the bottom left corner and top right corner point values are (1, 1) and (9, 8), respectively.

Input: points = (x1 = 0, y1 = 0 ), (x2 = 10, y1 = 0), (x3 = 10, y3 = 10), (x4 = 0, y4 = 10) and (x = 13, y = 13)
Output: No

The point (13, 13) does not lie inside the rectangle.

Example 1

The following program compares the given point (x = 2, y = 3) with (x1 = 1, x2 = 9 ) and (y1 = 1, y2 = 8), and displays whether the point lies inside the rectangle or not:

public class checkPoints {
   public static void main(String[] args) {

      int x1 = 1, y1 = 1;
      int x2 = 9, y2 = 8;
      int x = 2, y = 3;
      System.out.println("The given points are: ");
      System.out.println("(x1 = " + x1 + ", x2 = " + x2 + ")");
      System.out.println("(y1 = " + y1 + ", y2 = " + y2 + ")");
      System.out.println("(x = " + x + ", y = " + y + ")");

      if (x > x1 && x < x2 && y > y1 && y < y2) {
         System.out.println("Yes!, the Yes given point lies inside rectangle");
      }
      else{
         System.out.println("No!, the Yes given point lies inside rectangle");
      }
   }
}

The above program produces the following output:

The given points are: 
(x1 = 1, x2 = 9)
(y1 = 1, y2 = 8)
(x = 2, y = 3)
Yes!, the Yes given point lies inside rectangle

Example 2

This is another way to check whether a given point (x = 13, y = 13) lies inside a rectangle. We define a method checkPint() that compares the area of a rectangle with the sum of the areas of four triangles formed by the given point and the rectangle's vertices.

If the areas match, the point lies inside the rectangle; otherwise not.

public class rectangle {
   //method to calculate area of rectangle
   static float triangleArea(int x1, int y1, int x2, int y2, int x3, int y3) {
      return (float)Math.abs((x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0);
   }

   //method to check whether point lies inside rectangle
   static boolean checkPoint(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4, int x, int y) {

      //area of rectangle ABCD
      float ABCD = (x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))/2 + (x1*(y4-y3) + x4*(y3-y1) + x3*(y1-y4))/2;

      //find area of triangle PAB
      float PAB = triangleArea(x, y, x1, y1, x2, y2);

      //find area of triangle PBC
      float PBC = triangleArea(x, y, x2, y2, x3, y3);

      //find area of triangle PCD
      float PCD = triangleArea(x, y, x3, y3, x4, y4);

      // find area of triangle PAD
      float PAD = triangleArea(x, y, x1, y1, x4, y4);

      //check if area of rectangle is
      //equal to areas formed by four triangles
      if(ABCD == PAB + PBC + PCD + PAD){
         return true;
      }
      return false;
   }
   public static void main (String[] args) {
      int x1 = 0, x2 = 10, x3 = 10, x4 = 0;
      int y1 = 0, y2 = 0, y3 = 10, y4 = 10;
   
      //given point to be checked
      int x = 13;
      int y = 13;
      System.out.println("The points needs to be checked: x = " + x + ", y =  " + y);
      System.out.println("The rectangle four points are: ");
      System.out.println(
         "x1 = " + x1 +
         ", x2 = " + x2 +
         ", x3 = " + x3 +
         ", x4 = " + x4
      );
      System.out.println(
         "y1 = " + y1 +
         ", y2 = " + y2 +
         ", y3 = " + y3 +
         ", y4 = " + y4
      );
      boolean result = checkPoint(x1, y1, x2, y2, x3, y3, x4, y4, x, y);
      System.out.println("Is points the given points are lies inside the rectangle? " + result);
   }
}

Following is the output of the above program:

The points needs to be checked: x = 13, y =  13
The rectangle four points are: 
x1 = 0, x2 = 10, x3 = 10, x4 = 0
y1 = 0, y2 = 0, y3 = 10, y4 = 10
Is points the given points are lies inside the rectangle? false