Question

M (3, –6) is rotated 90° counterclockwise.

(x, y) → (–y, x)

1. Switch the x- and y-coordinates:
(6, –3)

2. Multiply the new x-coordinate by –1:
(6(–1), –3)

3. 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
.

Answer 1

Let's analyze the steps Mary Beth took to apply the 90° counterclockwise rotation rule to the point \( M(3, -6) \).

1. **Original Coordinates:**
The original coordinates are \( (3, -6) \).

2. **Applying the Mapping Rule:**
According to the mapping rule for a 90° counterclockwise rotation around the origin, the transformation is given by \( (x, y) \rightarrow (-y, x) \).

For point \( M(3, -6) \):
- The new x-coordinate will be \( -(-6) = 6 \).
- The new y-coordinate will be \( 3 \).

So, after applying the rule correctly, we should get:
\[
(3, -6) \rightarrow (6, 3)
\]

3. **Mary Beth's Steps:**
- She switched the coordinates to get \( (6, -3) \). This step is incorrect; while she attempted to switch the coordinates, she did not correctly apply the negative sign to the new y-coordinate.
- Next, she multiplied the new x-coordinate by -1, making it \( (6(-1), -3) \), which wrongly gives \( (-6, -3) \).

4. **Conclusion:**
The student made an error in both switching and applying the transformation. The correct rotation of point \( M(3, -6) \) results in the coordinates \( (6, 3) \), not \( (-6, -3) \).

So to summarize the final answer:
Mary Beth made errors in the switching of coordinates and in applying the mapping rule correctly. The correct coordinates after a 90° counterclockwise rotation should be \( (6, 3) \).