Question

1. a shape is transformed on a coordinate grid using the rule ((x, y) \to (y, -x)). which of the following describes this transformation? 8. 10c

a a reflection across the x - axis
b a reflection across the y - axis
c a rotation (90^circ) clockwise about the origin
d a rotation (90^circ) counter - clockwise about the origin

Explanation:

To determine the transformation, we analyze the coordinate rule \((x, y) \to (y, -x)\). Let's recall the rotation rules:

• A \(90^\circ\) counter - clockwise rotation about the origin has the rule \((x,y)\to(-y,x)\).
• A \(90^\circ\) clockwise rotation about the origin has the rule \((x,y)\to(y, - x)\).
• Reflection over the \(x\) - axis: \((x,y)\to(x, - y)\).
• Reflection over the \(y\) - axis: \((x,y)\to(-x,y)\).

Since the given rule \((x, y)\to(y, - x)\) matches the rule for a \(90^\circ\) clockwise rotation about the origin, the transformation is a \(90^\circ\) clockwise rotation about the origin.

Answer:

C. A rotation \(90^\circ\) clockwise about the origin