Given two integers X and Y. The task is to find two vertices of an isosceles triangle ABC(right-angled at B) which has one vertex at a point B(0, 0). And there is a rectangle with opposite sides (0, 0) and (X, Y). All the points of this rectangle are located inside or on the border of the triangle. Print 4 integers x1, y1, x2, y2, where A(x1, y1) and B(x2, y2).
Input : X = 3, Y = 3
Output : 6 0 0 6
Input : X = -3, y = -2
Output : -5 0 0 -5
Let Val = |x| + |y|. Then the first point is (Val * sign(x), 0) and the second point is (0, Val * sign(y)).
Let’s see how it works for x > 0 and y > 0. Other cases can be proved in a similar way.
We need to show, that (x, y) belongs to our triangle(including its borders). In fact (x, y) belongs to segment, connecting (x + y, 0) with (0, x + y). The line through (x + y, 0) and (0, x + y) is Y = – X + x + y. Using coordinates (x, y) in this equation proves our answer.
Below is the implementation of the above approach:
6 0 0 6
Time Complexity : O(1)
- Find the area of quadrilateral when diagonal and the perpendiculars to it from opposite vertices are given
- Find the altitude and area of an isosceles triangle
- Find the cordinates of the fourth vertex of a rectangle with given 3 vertices
- Maximum number of 2x2 squares that can be fit inside a right isosceles triangle
- Maximum number of squares that can fit in a right angle isosceles triangle
- Divide an isosceles triangle in two parts with ratio of areas as n:m
- Area of largest triangle that can be inscribed within a rectangle
- Area of a triangle inscribed in a rectangle which is inscribed in an ellipse
- Find two disjoint good sets of vertices in a given graph
- Find the number of distinct pairs of vertices which have a distance of exactly k in a tree
- Find minimum area of rectangle with given set of coordinates
- Ratio of area of a rectangle with the rectangle inscribed in it
- Largest subset of rectangles such that no rectangle fit in any other rectangle
- Program to find Perimeter / Circumference of Square and Rectangle
- Find if there exists multiple ways to draw line through (x, y) to cut rectangle in equal halfs
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. 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.