Question

1. the coordinate grid below shows rectangle wxyz. 8.10c

rectangle wxyz is rotated 270° counter - clockwise about the origin to create rectangle wxyz. which rule describes this transformation.
a ((x,y)\to(-x,y))
b ((x,y)\to(x,-y))
c ((x,y)\to(-y,x))
d ((x,y)\to(y,-x))

Explanation:

Step1: Recall rotation rules

The rule for a \(270^\circ\) counter - clockwise rotation about the origin is that a point \((x,y)\) is transformed to \((y, - x)\). Let's also recall other rotation rules for clarity:

• \(90^\circ\) counter - clockwise: \((x,y)\to(-y,x)\)
• \(180^\circ\) counter - clockwise: \((x,y)\to(-x,-y)\)
• \(270^\circ\) counter - clockwise: \((x,y)\to(y, - x)\) (which is equivalent to a \(90^\circ\) clockwise rotation)

Let's analyze each option:

• Option A: \((x,y)\to(-x,y)\) is the rule for a reflection over the \(y\) - axis, not a \(270^\circ\) counter - clockwise rotation.
• Option B: \((x,y)\to(x,-y)\) is the rule for a reflection over the \(x\) - axis, not a \(270^\circ\) counter - clockwise rotation.
• Option C: \((x,y)\to(-y,x)\) is the rule for a \(90^\circ\) counter - clockwise rotation, not a \(270^\circ\) counter - clockwise rotation.
• Option D: \((x,y)\to(y, - x)\) matches the rule for a \(270^\circ\) counter - clockwise rotation about the origin.

Answer:

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