A rotation matrix is a 2x2 matrix that defines a linear transformation that rotates a vector around the origin by a certain angle. To rotate an object or image by 90 degrees clockwise, you can use a rotation matrix or a transformation matrix. This type of rotation changes the orientation of the object or image by 90 degrees in a clockwise direction, which means that the top edge of the object or image becomes the right edge, the right edge becomes the bottom edge, the bottom edge becomes the left edge, and the left edge becomes the top edge. Rotating an object or image by 90 degrees clockwise is a common operation in computer graphics and image processing. In summary, the 90 degree clockwise rotation is a useful transformation in geometry and computer graphics, and can be easily achieved using matrix multiplication or a sequence of reflection and coordinate swapping steps. Therefore, the rotated triangle has vertices (-1, 1), (-3, -1), and (-4, 2), as shown in the figure below: What Is The Rule For Rotating A Point 90 Degrees? Using the matrix multiplication rule, we can calculate the new coordinates of each vertex as follows: The resulting figure is the 90 degree clockwise rotation of the original figure.įor example, suppose we want to rotate the triangle with vertices (1, 1), (3, 1), and (2, 4) 90 degrees clockwise about the origin.Swap the x and y coordinates of each point.This matrix transformation can also be represented by the following sequence of steps: The 90 degree clockwise rotation rule states that to rotate a figure 90 degrees clockwise around a fixed point, each point of the figure must be transformed by the following matrix multiplication: In other words, each point in the figure is rotated 90 degrees in a clockwise direction about the point of rotation. What Is The Rule For Rotating 90 Degrees Clockwise About The Origin?Ī 90 degree clockwise rotation is a geometric transformation that rotates a figure or object 90 degrees in a clockwise direction around a fixed point. Therefore, the final result of rotating the point (2, 5) 90 degrees clockwise about the fixed point (1, 1) is (-3, 2). Step 3: Translate the rotated point back to its original position by adding the fixed point's coordinates: (-4 + 1, 1 + 1) = (-3, 2) Step 2: Rotate the translated point (1, 4) 90 degrees clockwise about the origin using the rule we mentioned earlier: New x-coordinate = -y = -(4) = -4 New y-coordinate = x = 1 Therefore, the rotated point is (-4, 1). Step 1: Translate the fixed point (1, 1) to the origin by subtracting its coordinates from the point we want to rotate: (2 - 1, 5 - 1) = (1, 4) Translate the rotated point back to its original position.įor example, let's say we want to rotate the point (2, 5) 90 degrees clockwise about the fixed point (1, 1).Rotate the point 90 degrees clockwise about the origin using the rule mentioned above.Translate the fixed point to the origin.
To rotate a point 90 degrees about a fixed point (not necessarily the origin), we need to perform three steps: Therefore, the new point after rotation is (-4, 3).
New x-coordinate = -y = -(4) = -4 New y-coordinate = x = 3 To do so, we switch the x and y coordinates and negate the new x coordinate:
In other words, if the original point is (x, y), the new point after rotation will be (-y, x).įor example, let's say we want to rotate the point (3,4) 90 degrees clockwise about the origin. When rotating a point 90 degrees clockwise about the origin, we switch the x and y coordinates of the point and negate the new x coordinate.
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