Question

what transformation is described by the rule (x, y) → (-x, y)?
a. rotation
b. reflection over the y-axis
c. translation
d. reflection over the x-axis

Explanation:

Step1: Recall transformation rules

• Reflection over y - axis: The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\).
• Reflection over x - axis: The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, - y)\).
• Translation: Involves shifting the point \((x,y)\) by adding or subtracting constants to \(x\) and \(y\) (e.g., \((x,y)\to(x + a,y + b)\) where \(a,b\) are constants).
• Rotation: For example, a 90 - degree rotation about the origin has different rules (e.g., \((x,y)\to(-y,x)\) for 90 - degree counter - clockwise rotation), which is different from \((x,y)\to(-x,y)\).

Step2: Match the given rule with transformation types

The given transformation rule is \((x,y)\to(-x,y)\). By comparing with the rules of different transformations, we see that this matches the rule for reflection over the \(y\) - axis.

Answer:

b. Reflection over the y - axis