Question

choose the general rule below that describes the reflection mapping △def to △def. (x,y)→(−y,x) (x,y)→(y,x) (x,y)→(−x,−y) (x,y)→(−x,y) (x,y)→(x,−y) (x,y)→(−y,−x) (x,y)→(y,−x)

Explanation:

Step1: Recall reflection rules

In a reflection, we transform a point $(x,y)$ based on the axis of reflection. A reflection across the $y$-axis changes the sign of the $x$-coordinate while keeping the $y$-coordinate the same. The general rule for a reflection across the $y$-axis is $(x,y)\to(-x,y)$.

Step2: Analyze options

We check each option:

• $(x,y)\to(-y,x)$ is a rotation - not a reflection we need.
• $(x,y)\to(y,x)$ is a reflection across $y = x$.
• $(x,y)\to(-x,-y)$ is a rotation of $180^{\circ}$ about the origin.
• $(x,y)\to(-x,y)$ is a reflection across the $y$-axis.
• $(x,y)\to(x,-y)$ is a reflection across the $x$-axis.
• $(x,y)\to(-y,-x)$ is a rotation - not the required reflection.
• $(x,y)\to(y,-x)$ is a reflection across $y=-x$.

Answer:

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