Given three coordinates (x, y), which are the midpoint of the sides of the triangle. The task is to find the coordinates of the triangle.
Input : midx1 = 5, midy1 = 3 midx2 = 4, midy2 = 4 midx3 = 5, midy3 = 5 Output : x1 = 4 y1 = 2 x2 = 4 y2 = 6 x3 = 6 y3 = 4 Solution can be verified by the figure.
Let’s separately solve for X-coordinates and Y-coordinates. For X coordinate of vertices, let them be x1, x2, x3. Then, X-coordinate of middel points will be (x1 + x2)/2, (x2 + x3)/2, (x3 + x1)/2. Observe, sum of these 3 expressions is equal to sum of X-coordinates. Now, we have sum of 3 varibles and 3 expressions for sum of every pair of them, find out the values of coordinates by solving equations.
Similarly, we solve for Y-coordinates.
Below is the implemenetation of this approach:
6 4 4 2 4 6
Time Complexity : O(1)
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