Question

△lmn is rotated 180° counterclockwise about the origin to produce △lmn. write the rule for the rotation. (x, y) ↦ (\square, \square)

Explanation:

Step1: Recall 180° rotation rule

A 180° counterclockwise (or clockwise) rotation about the origin has the rule: for a point \((x, y)\), the image after rotation is \((-x, -y)\). This is because rotating 180° flips both the x - coordinate and y - coordinate across the origin, changing their signs.

Step2: Apply the rule to the problem

Given the rotation of \(\triangle LMN\) 180° counterclockwise about the origin to get \(\triangle L'M'N'\), the rule for the transformation of any point \((x, y)\) in \(\triangle LMN\) to its corresponding point \((x', y')\) in \(\triangle L'M'N'\) is \((x, y)\to(-x, -y)\).

Answer:

\((x, y)\to\boldsymbol{(-x, -y)}\)