Reviewed by Jessica Kaminski
What is the algebraic rule for a figure that is rotated 270° clockwise about the origin?
Answer: The algebraic rule for a figure that is rotated 270° clockwise about the origin is (x, y) → (–y, x)
Rotating a figure in the coordinate plane involves changing the positions of its points according to a specific rule. When a point or figure is rotated 270° clockwise about the origin, each point in the figure is moved in a way that can be described algebraically. Understanding this rule will help in performing rotations quickly without drawing.
Methods
Math Tutor Explanation Using Coordinate Rules
Algebraic rules for rotations are based on manipulating the x and y values of each point. For a 270° clockwise rotation, follow these steps:
Step 1: Step 1: Swap the x- and y-values of the original point (x, y)
Step 2: Step 2: Change the sign of the new x-value (which is the original y-value), giving you the new coordinates (–y, x)
Math Tutor Explanation Using Degrees and Counterclockwise Rotation
Remember that a 270° clockwise rotation is the same as a 90° counterclockwise rotation. The algebraic result for rotating a point 90° counterclockwise about the origin is the same:
Step 1: Step 1: Rotate the point (x, y) 90° counterclockwise to get (–y, x)
Step 2: Step 2: Conclude that (x, y) → (–y, x) is the rule for both 270° clockwise and 90° counterclockwise rotations
Step 1:
Step 2:
Math Tutor suggests: Mastering Rotations and Transformations in Geometry
Want to strengthen your understanding of geometric transformations, especially rotations about the origin? Check out these related questions for more practice and insights.
FAQ on Rotations in the Coordinate Plane
How do you rotate a point 270° clockwise about the origin?
Replace (x, y) with (–y, x)
Is rotating 270° clockwise the same as rotating 90° counterclockwise?
Yes, both result in (x, y) → (–y, x)
What is the rule for rotating a point 90° clockwise?
Change (x, y) to (y, –x)
How can I remember the rotation rules?
Associate each degree of rotation with its coordinate transformation: 90° clockwise (y, –x), 180° (–x, –y), 270° clockwise or 90° counterclockwise (–y, x)
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