Question

identify the mapping description that best describes the rotation. enter the option number of the correct answer. option #1: (x,y)→(y,x) option #2: (x,y)→(y, - x) option #3: (x,y)→(-y,x) option #4: (x,y)→(-x, - y)

Explanation:

Step1: Identify coordinates of a point

Let's take point $Q(0,1)$. After rotation, $Q'$ has coordinates $(1,0)$.

Step2: Test the mapping rules

For Option #1: If $(x,y)=(0,1)$, then $(y,x)=(1,0)$.
For Option #2: If $(x,y)=(0,1)$, then $(y, - x)=(1,0)$ also works for this point. But let's check another point. Take $P(-3,-2)$. Its image $P'$ has coordinates $(-2,3)$. For Option #1: If $(x,y)=(-3,-2)$, then $(y,x)=(-2,-3)$ (wrong). For Option #2: If $(x,y)=(-3,-2)$, then $(y,-x)=(-2,3)$ (correct).
For Option #3: If $(x,y)=(-3,-2)$, then $(-y,x)=(2,-3)$ (wrong).
For Option #4: If $(x,y)=(-3,-2)$, then $(-x,-y)=(3,2)$ (wrong).

Answer:

Option #2. $(x,y)\to(y, - x)$