How to rotate points 90 degrees?
Understand the Problem
The question is asking for the method to rotate points in a coordinate system by 90 degrees. This involves using certain mathematical formulas or transformations based on the coordinates of the points.
Answer
The new coordinates after rotating the point $(x, y)$ by 90 degrees counterclockwise are $(-y, x)$.
Answer for screen readers
The new coordinates after rotating the point $(x, y)$ by 90 degrees counterclockwise are $(-y, x)$.
Steps to Solve
- Identify the Original Coordinates
Let the original point be represented as $(x, y)$.
- Write the Rotation Formula
To rotate a point $(x, y)$ by 90 degrees counterclockwise around the origin, we use the transformation:
$$(x', y') = (-y, x)$$
- Apply the Formula
Substituting the original coordinates into the rotation formula, we calculate the new coordinates:
- If the original point is $(x, y)$, the new point after a 90-degree rotation will be:
$$ x' = -y $$ $$ y' = x $$
- Example Calculation
For example, if we have the point $(2, 3)$:
- New coordinates will be: $$ x' = -3 $$ $$ y' = 2 $$
Thus, the point $(2, 3)$ becomes $(-3, 2)$ after a 90-degree counterclockwise rotation.
The new coordinates after rotating the point $(x, y)$ by 90 degrees counterclockwise are $(-y, x)$.
More Information
This rotation is commonly used in geometry and computer graphics, allowing for the adjustment of points in a coordinate system. Understanding these transformations is essential for working with shapes and motion in 2D space.
Tips
- Forgetting the Sign Change: When rotating 90 degrees counterclockwise, it’s essential to remember that the x-coordinate becomes negative. Ensure to follow the formula correctly.
- Confusing the Order: Remember that the new x-coordinate is taken from the old y-coordinate, and the new y-coordinate is taken from the old x-coordinate.
