How to Perform a 90-Degree Clockwise Rotation for a Shape: Step-by-Step Guide

Rotation 90 degrees clockwise

To rotate a shape or object 90 degrees clockwise, each point of the shape needs to be reflected across the y-axis and then swapped with its corresponding x-coordinate

To rotate a shape or object 90 degrees clockwise, each point of the shape needs to be reflected across the y-axis and then swapped with its corresponding x-coordinate.

Here are the steps to perform a 90-degree clockwise rotation:

1. Write down the coordinates of each point of the original shape.
Let’s say the original shape has points (x1, y1), (x2, y2), (x3, y3), … (xn, yn).

2. Reflect each point across the y-axis.
The reflection of a point (x, y) across the y-axis gives us (-x, y).
So, the reflected points for our example are (-x1, y1), (-x2, y2), (-x3, y3), … (-xn, yn).

3. Swap the x and y coordinates for each reflected point.
After swapping the coordinates, we get (y1, -x1), (y2, -x2), (y3, -x3), … (yn, -xn).

4. Now, we have the new coordinates for the rotated shape.
Connect the points with lines to see the new shape after the 90-degree clockwise rotation.

For example, let’s rotate a square with vertices A (2, 2), B (4, 2), C (4, 4), and D (2, 4) 90 degrees clockwise:

1. The original square:
A (2, 2)
B (4, 2)
C (4, 4)
D (2, 4)

2. Reflect each point across the y-axis:
A (-2, 2)
B (-4, 2)
C (-4, 4)
D (-2, 4)

3. Swap the x and y coordinates:
A (2, -2)
B (2, -4)
C (4, -4)
D (4, -2)

4. Connect the new points to form the rotated square:
The rotated square has vertices A’ (2, -2), B’ (2, -4), C’ (4, -4), and D’ (4, -2).

This is how you can perform a 90-degree clockwise rotation for a shape or object. Keep in mind that the process may differ for different types of rotations or shapes, but the idea of reflecting and swapping coordinates remains the same.

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