Question

1. the coordinate grid shows parallelogram pqrs.

parallelogram pqrs is rotated 90° clockwise about the origin to create parallelogram pqrs. which rule describes this transformation?
○ (x,y) → (x, −y) ○ (x,y) → (−x, y)
○ (x,y) → (y, x) ○ (x,y) → (y, −x)

Explanation:

Step1: Recall Rotation Rules

The rule for a \(90^\circ\) clockwise rotation about the origin is \((x, y) \to (y, -x)\). Let's verify with a point. Take a vertex of the parallelogram, say \(R\) (from the graph, approximate coordinates: let's assume \(R\) is at \((-1, 7)\)).

Step2: Apply Each Rule

• For \((x,y)\to(x, -y)\): \((-1,7)\to(-1, -7)\) (not \(90^\circ\) clockwise).
• For \((x,y)\to(-x, y)\): \((-1,7)\to(1, 7)\) (not \(90^\circ\) clockwise).
• For \((x,y)\to(y, x)\): \((-1,7)\to(7, -1)\) (this is \(90^\circ\) counter - clockwise).
• For \((x,y)\to(y, -x)\): \((-1,7)\to(7, 1)\) (this is \(90^\circ\) clockwise).

Answer:

\((x, y) \to (y, -x)\)