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)
- Reflection of a point about a line in C++
- Rotation of a point about another point in C++
- First collision point of two series
- Triangle with no point inside
- Mirror of a point through a 3 D plane
- Distance between a point and a Plane in 3 D
- Find the other end point of a line with given one end and mid
- Check whether given floating point number is even or odd
- Program to find the Break Even Point
- Perpendicular distance between a point and a Line in 2 D
- Check if a point is inside, outside or on the parabola
- Find normal at a given point on the curve
- Finding the best fit rectangle that covers a given point
- Program to find the mid-point of a line
- Check if a point is inside, outside or on the ellipse
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.