Question

rule 2
old → new
(1,1) → (-1,-1)
(3,5) → (-3,-5)
(5,7) → (-5,-7)
this is a 180 degree counterclockwise rotation around the origin.
can you write the rule?
the rule is (x,y) →...

Explanation:

Step1: Analyze Coordinate Changes

For each point \((x,y)\), the old coordinates and new coordinates are given: \((1,1)\to(-1,-1)\), \((3,5)\to(-3,-5)\), \((5,7)\to(-5,-7)\). Observe that the \(x\)-coordinate and \(y\)-coordinate of each new point are the negatives of the old ones.

Step2: Formulate the Rule

From the pattern, if we have a point \((x,y)\), after a 180 - degree counterclockwise (or clockwise, since 180 - degree rotation in either direction around the origin has the same effect) rotation around the origin, the new coordinates \((x',y')\) satisfy \(x'=-x\) and \(y'=-y\). So the rule is \((x,y)\to(-x,-y)\).

Answer:

\((-x, -y)\)