To determine the algebraic rule for rotating a figure 270 degrees clockwise about the origin, we first need to understand how rotation affects the coordinates of points in a plane.
When a point (x, y) is rotated 270 degrees clockwise, the transformation of its coordinates can be found using the following rule:
(x, y) → (y, -x)
This means that the x-coordinate of the original point becomes the y-coordinate of the new point, and the y-coordinate of the original point becomes the negative x-coordinate in the new position.
For example, if we take the point (2, 3) and rotate it 270 degrees clockwise around the origin, we can apply the rule:
- Original point: (2, 3)
- After rotation: (3, -2)
This transformation can be visualized more easily by considering the rotation direction. Starting from the positive x-axis, rotating 90 degrees takes us to the positive y-axis, another 90 degrees (180 total) takes us to the negative x-axis, 270 degrees brings us to the negative y-axis, thus confirming our algebraic rule.
In summary, the algebraic rule for a 270-degree clockwise rotation about the origin is simply:
(x, y) → (y, -x)
This rule can be applied to any point in the coordinate plane, enabling you to find the new location of that point after the rotation.