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:
# Python3 Program for find the 180
# degree reflection of one point
# around another point.
def findPoint(x1, y1, x2, y2):
print(“(” , 2 * x2 – x1 , “,”,
2 * y2 – y1 ,”)”);
# Driver Code
x1 = 0;
y1 = 0;
x2 = 1;
y2 = 1;
findPoint(x1, y1, x2, y2);
# This code is contributed by mits
Time Complexity : O(1)
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