Question

m (3, −6) is rotated 90° counterclockwise.
(x, y) → (−y, x)

1. switch the x- and y-coordinates:

(6, −3)

1. multiply the new x-coordinate by −1:

(6(−1), −3)

1. simplify:

(−6, −3)
mary beth used the mapping rule to find the coordinates of a point that had been rotated 90° counterclockwise around the origin.
examine the steps to determine whether she made an error.
the student made

Explanation:

Step1: Identify original point

Original point: $M(3, -6)$

Step2: Apply 90° CCW rotation rule

Rule: $(x, y) \to (-y, x)$
Substitute $x=3$, $y=-6$:
$-y = -(-6) = 6$, $x=3$
Result: $(6, 3)$

Step3: Compare with student's work

Student incorrectly used $(6, -3)$ as swapped coordinates, then multiplied wrong value.

Answer:

The student made an error. The correct rotated coordinates are $(6, 3)$, while the student incorrectly swapped the coordinates and applied the sign change to the wrong value, resulting in $(-6, -3)$.