How to rotate a shape 90 degrees clockwise?
Understand the Problem
The question is asking for instructions on how to perform a 90-degree clockwise rotation of a geometric shape. It seeks to understand the steps or methods involved in achieving this transformation mathematically or visually.
Answer
(x', y') = (y, -x)
Answer for screen readers
To rotate a shape 90 degrees clockwise, use the transformation (x', y') = (y, -x) for each vertex of the shape.
Steps to Solve
- Identify the coordinates of the shape
Write down the coordinates of each vertex of the shape. For example, suppose we have a quadrilateral with vertices at (x1, y1), (x2, y2), (x3, y3), and (x4, y4).
- Use the rotation formula
To rotate a point (x, y) 90 degrees clockwise about the origin, use the transformation:
$$ (x', y') = (y, -x) $$
For each vertex of the shape, substitute the coordinates into the formula.
- Calculate new coordinates
Compute the new coordinates for each vertex using the formula. For instance, if our original vertex is (x1, y1), the new coordinates will be:
$$ x' = y1 $$ $$ y' = -x1 $$
Repeat this calculation for each vertex of the shape.
- Plot the new coordinates
Plot the new set of coordinates on the coordinate plane to visualize the rotated shape.
To rotate a shape 90 degrees clockwise, use the transformation (x', y') = (y, -x) for each vertex of the shape.
More Information
Rotating a point (x, y) 90 degrees clockwise results in swapping the coordinates and negating the new y-coordinate.
Tips
A common mistake when performing rotations is mixing up clockwise and counterclockwise directions. Make sure to apply the correct transformation formula for the intended direction.
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