Question

an architect is designing a new windmill with four sails. in her sketch, the sails center of rotation is the origin, (0,0), and the tip of one of the sails, point r, has coordinates (-6,9). she wants to make another sketch that shows the windmill after the sails have rotated 180° about their center of rotation. what would be the coordinates of r? the coordinates of r would be \boxed{}. (type an ordered pair.)

Explanation:

Step1: Recall rotation 180° rule

To rotate a point \((x, y)\) 180° about the origin, the rule is \((x, y) \to (-x, -y)\).

Step2: Apply the rule to point R

Given point \(R\) has coordinates \((-6, 5)\). Using the 180° rotation rule, we substitute \(x = -6\) and \(y = 5\) into \((-x, -y)\). So, \(-x = -(-6) = 6\) and \(-y = -5\).

Answer:

\((6, -5)\)