How to rotate a point 90 degrees counterclockwise?
Understand the Problem
The question is asking for the method to rotate a given point in a coordinate system 90 degrees counterclockwise. This involves applying a transformation to the coordinates of the point based on rotation principles in mathematics.
Answer
The new coordinates after rotating the point $(x, y)$ 90 degrees counterclockwise are $(-y, x)$.
Answer for screen readers
The new coordinates after rotating the point $(x, y)$ 90 degrees counterclockwise are $(-y, x)$.
Steps to Solve
- Identify the original coordinates
Let's say the original point is given as $(x, y)$.
- Apply the rotation formula
To rotate a point 90 degrees counterclockwise, we can use the following transformation:
- The new coordinates $(x', y')$ will be calculated using:
$$ x' = -y $$ $$ y' = x $$
- Substitute the original coordinates
Now, substitute the original coordinates $(x, y)$ into the transformation equations:
$$ x' = -y $$ $$ y' = x $$
- Write down the new coordinates
After substituting the original coordinates, we can express the new coordinates as:
- The rotated point will be $(x', y')$.
The new coordinates after rotating the point $(x, y)$ 90 degrees counterclockwise are $(-y, x)$.
More Information
This transformation is based on the properties of rotation in the Cartesian coordinate system. Rotating points is commonly used in geometric transformations and has applications in computer graphics.
Tips
- Confusing the direction of rotation: Ensure you are rotating counterclockwise. Rotating clockwise requires different equations.
- Swapping x and y: Remember which coordinate becomes which in the transformation.
