Given two numbers a and b where b < a form a rectangle with points (0, b), (b, 0), (a-b, b), (b, a-b). Given a point (x, y), the task is to check whether this point lies inside or on the rectangle or not.
Input: a = 7, b = 2, x = 5, y = 2; Output: Given point does not lie on the rectangle Input: a = 7, b = 2, x = 4, y = 5; Output: Given point lies inside the rectangle
Approach: An efficient way is to form 4 line’s equation of a rectangle. Then, if a given point lies in or on the rectangle if and only if, substituting the given point on:
- The right sideline ( x-y-b = 0 ) must give the value less than or equals to zero.
- The left sideline ( x-y+a = 0 ) must give the value greater than or equals to one.
- The upper sideline ( x+y-2*a+b = 0 ) must give the value less than or equals to zero.
- The lower sideline ( x+y-b = 0 ) must give the value greater than or equals to one.
Given point lies inside the rectangle
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.
- Check if a point lies on or inside a rectangle | Set-2
- Check whether a given point lies inside a rectangle or not
- How to check if a given point lies inside or outside a polygon?
- Check whether a point lies inside a sphere or not
- Check whether a given point lies inside a triangle or not
- Check if the given point lies inside given N points of a Convex Polygon
- Find a point that lies inside exactly K given squares
- Find if a point lies inside a Circle
- Find if a point lies inside, outside or on the circumcircle of three points A, B, C
- Check whether the point (x, y) lies on a given line
- Check if a given circle lies completely inside the ring formed by two concentric circles
- Check if a point is inside, outside or on the parabola
- Check if a point is inside, outside or on the ellipse
- Check if any point overlaps the given Circle and Rectangle
- Check if a circle lies inside another circle or not
- Count of integral coordinates that lies inside a Square
- Coordinates of rectangle with given points lie inside
- Sum of Area of all possible square inside a rectangle
- Count the number of rhombi possible inside a rectangle of given size
- Triangle with no point inside
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.