Given two points coordinates (x1, y1) and (x2, y2)on 2D plane. The task is to find the reflection of (x1, y1) at 180 degree rotation of (x2, y2).
Input : x1 = 0, y1 = 0, x2 = 1, y2 = 1 Output : (2, 2) Input : x1 = 1, y1 = 1, x2 = 2, y2 = 2 Output : (3, 3)
Let the reflection point of point (x1, y1) about (x2, y2) be (x’, y’).
For (x’, y’) be the 180 degree rotation of point (x1, y1) around point (x2, y2), they all must be collinear i.e all the three point must lie on a same straight line. Also, observe (x2, y2) will became mid point between (x1, y1) and (x’, y’).
x’ – x2 = x2 – x1
y’ – y2 = y2 – y1
x’ = 2 * x2 – x1
y’ = 2 * y2 – y1
Below is the implementation of this approach:
Time Complexity : O(1)
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