__How to Check if a Given Point Lies Inside a Triangle in Java__

### Understanding the Problem

### The Barycentric Coordinate System

### Computing the Area of a Triangle

### Checking if the Point Lies Inside

### Implementing the Algorithm in Java

```
class Triangle {
private Point pointA;
private Point pointB;
private Point pointC;
public Triangle(Point point1, Point point2, Point point3) {
this.pointA = point1;
this.pointB = point2;
this.pointC = point3;
}
public float getArea() {
return Math.abs((pointA.X * (pointB.Y-> pointC.Y) + pointB.X
* (pointC.Y-> pointA.Y) + pointC.X * (pointA.Y-> pointB.Y))
/ (float) 2.0);
}
}
public static boolean isPointInsideTriangle(Triangle triangle1,
Triangle triangle2, Triangle triangle3, Triangle triangle4) {
float area = triangle2.getArea() + triangle3.getArea()
+ triangle4.getArea();
if (triangle1.getArea() == area) {
return true;
} else {
return false;
}
}
```

### Unit Tests

Here is the unit test for this program which can also run to play with it:

```
import org.junit.jupiter.api.Test;
import static org.junit.jupiter.api.Assertions.*;
public class TriangleTest {
@Test
public void testPointInsideTriangle() {
Point A = new Point(0, 0);
Point B = new Point(4, 0);
Point C = new Point(2, 3);
Triangle triangle1 = new Triangle(A, B, C);
// Point (2, 1) lies inside the triangle (A, B, C)
Point P1 = new Point(2, 1);
assertTrue(isPointInsideTriangle(triangle1, new Triangle(A, B, P1),
new Triangle(B, C, P1), new Triangle(C, A, P1)));
// Point (3, 2) lies inside the triangle (A, B, C)
Point P2 = new Point(3, 2);
assertTrue(isPointInsideTriangle(triangle1, new Triangle(A, B, P2),
new Triangle(B, C, P2), new Triangle(C, A, P2)));
}
@Test
public void testPointOutsideTriangle() {
Point A = new Point(0, 0);
Point B = new Point(4, 0);
Point C = new Point(2, 3);
Triangle triangle1 = new Triangle(A, B, C);
// Point (1, 1) lies outside the triangle (A, B, C)
Point P1 = new Point(1, 1);
assertFalse(isPointInsideTriangle(triangle1, new Triangle(A, B, P1),
new Triangle(B, C, P1), new Triangle(C, A, P1)));
// Point (5, 3) lies outside the triangle (A, B, C)
Point P2 = new Point(5, 3);
assertFalse(isPointInsideTriangle(triangle1, new Triangle(A, B, P2),
new Triangle(B, C, P2), new Triangle(C, A, P2)));
}
}
```

That's all about **how to check if a given point is inside a triangle or not in Java**. Understanding the mathematical concepts behind checking if a given point lies inside a triangle makes it easier to code the algorithm in Java and we have created an efficient and reliable solution. Utilizing the Barycentric Coordinate System and calculating triangle areas, we can accurately determine if a point resides within a triangle or not.

With the aid of comprehensive unit tests, we have validated the correctness of our implementation across various scenarios. This technique is a valuable addition to a Java developer's toolkit for computational geometry problems and can find applications in a wide range of fields, from computer graphics to robotics and beyond.

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