Question

1. which of the following produces the same algebraic rule as a rotation 270 degrees counterclockwise about the origin? a rotation 270 degrees clockwise about the origin a rotation 90 degrees clockwise about the origin a reflection across the x - axis a rotation 180 degrees clockwise about the origin

Explanation:

To determine which transformation has the same algebraic rule as a 270° counterclockwise rotation about the origin, we analyze rotation rules:

• A 270° counterclockwise rotation rule is \((x,y) \to (y, -x)\).
• A 90° clockwise rotation is equivalent to a 270° counterclockwise rotation (since \(360^\circ - 270^\circ = 90^\circ\) clockwise, and the rule for 90° clockwise is also \((x,y) \to (y, -x)\)).
• A 270° clockwise rotation has a different rule (\((x,y) \to (-y, x)\)).
• A reflection over the \(x\)-axis has rule \((x,y) \to (x, -y)\), which is different.
• A 180° clockwise rotation has rule \((x,y) \to (-x, -y)\), which is different.

Answer:

B. A rotation 90 degrees clockwise about the origin