Question

rule 3
old → new
(1,3) → (3,−1)
(3,7) → (7,−3)
(5,7) → (7,−5)
this is a 270 degree counterclockwise rotation around the origin.
can you write the rule?
the rule is (x,y) →...

Explanation:

Step1: Recall rotation rule

For a 270° counterclockwise rotation about the origin, the transformation rule is \((x,y)\to(y, -x)\). Let's verify with given points.

Step2: Verify with \((1,3)\)

Applying the rule: \(x = 1\), \(y = 3\) → \((3, -1)\), which matches the new point \((3, -1)\).

Step3: Verify with \((3,7)\)

\(x = 3\), \(y = 7\) → \((7, -3)\), matches the new point \((7, -3)\).

Step4: Verify with \((5,7)\)

\(x = 5\), \(y = 7\) → \((7, -5)\), matches the new point \((7, -5)\).

Answer:

\((y, -x)\)