Given a pentagon with vertex $B$ at $(2,3)$, what are the coordinates of $B\text{'}$ after the pentagon is rotated $90°$ counterclockwise about the origin?

• A. $(-3,2)$
• B. $(2,-3)$
• C. $(-2,-3)$
• D. $(3,-2)$

Answer: (A)

Verified step by step guidance

1. Identify the original coordinates of vertex B, which are given as \( (2, 3) \).
2. Recall the rule for rotating a point \( (x, y) \) by 90 degrees counterclockwise about the origin: the new coordinates become \( (-y, x) \).
3. Apply this rotation rule to the point \( (2, 3) \) by substituting \( x = 2 \) and \( y = 3 \) into the formula, resulting in \( (-3, 2) \).
4. Interpret the new coordinates \( (-3, 2) \) as the location of vertex \( B' \) after the rotation.
5. Verify that the rotation preserves the distance from the origin and the orientation is counterclockwise, confirming the correctness of the transformation.