A triangle is rotated $90°$ counterclockwise about the origin. Which rule describes the transformation of a point $(x,y)$?

• A. $(x,y)$
• B. $(-y,x)$
• C. $(-x,-y)$
• D. $(y,-x)$

Answer: (B)

Verified step by step guidance

1. Recall that a rotation of a point \((x, y)\) about the origin by an angle \(\theta\) counterclockwise can be described using the rotation formulas: \[ x' = x \cos \theta - y \sin \theta \] \[ y' = x \sin \theta + y \cos \theta \].
2. Substitute \(\theta = 90^\circ\) into the formulas. Since \(\cos 90^\circ = 0\) and \(\sin 90^\circ = 1\), the equations become: \[ x' = x \cdot 0 - y \cdot 1 = -y \] \[ y' = x \cdot 1 + y \cdot 0 = x \].
3. Therefore, the coordinates of the point after a 90-degree counterclockwise rotation are \((-y, x)\).
4. This means the transformation rule for any point \((x, y)\) under this rotation is: \[ (x, y) \to (-y, x) \].
5. Compare this result with the given options to identify the correct transformation rule.