Question

question
the point $(x,y)$ is first rotated $180^{circ}$ clockwise about the origin, translated 6 units to the left, and then reflected across the line $y = x$.
write a function $s$ to represent the sequence of transformations applied to the point $(x,y)$.
$s(x,y)=$

Explanation:

Step1: Rotate 180° clockwise

When a point \((x,y)\) is rotated \(180^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(-x,-y)\).

Step2: Translate 6 units left

After rotation, when we translate the point \((-x,-y)\) 6 units to the left (using the rule \((a,b)\to(a - h,b)\) where \(h = 6\)), we get \((-x-6,-y)\).

Step3: Reflect across \(y = x\)

When we reflect the point \((-x - 6,-y)\) across the line \(y=x\) (using the rule \((a,b)\to(b,a)\)), we get \((-y,-x - 6)\).

Answer:

\(S(x,y)=(-y,-x - 6)\)