Question
Mira uses the mapping rule to find the coordinate of a point that had been rotated 90° clockwise about the origin. Examine Mira’s solution to determine which step has an error.
M(–5, –6) is rotated 90° clockwise.
Step 1. Use the rule (x, y)g(y, –x).
Step 2. Switch x and y coordinates:
(–6, –5)
Step 3. Multiply the new x-coordinate by –1:
((–1)–6, –5)
Step 4. Simplify:
(6, –5)
Mira made an error in Step
.
M(–5, –6) is rotated 90° clockwise.
Step 1. Use the rule (x, y)g(y, –x).
Step 2. Switch x and y coordinates:
(–6, –5)
Step 3. Multiply the new x-coordinate by –1:
((–1)–6, –5)
Step 4. Simplify:
(6, –5)
Mira made an error in Step
.
Answers
GPT-4o mini
Let's examine Mira's solution step by step to identify the error:
1. **Step 1**: She states the rule for a 90° clockwise rotation as \((x, y) \rightarrow (y, -x)\). This is correct.
2. **Step 2**: She refers to switching the x and y coordinates. The original point M is \((-5, -6)\). According to the rotation rule, applying it should give:
\[
(x, y) = (-5, -6) \rightarrow (y, -x) = (-6, 5)
\]
However, Mira incorrectly states that this step results in \((-6, -5)\). This is where the first error occurs.
3. **Step 3**: Mira then states she multiplies the new x-coordinate by \(-1\), implying she was about to convert \(-6\) to \(6\). However, because she made an error in Step 2, her new x-coordinate is actually incorrect.
4. **Step 4**: Simplifying her erroneous coordinates \((6, -5)\) is also incorrect because she started with incorrect coordinates.
The error in Mira's solution occurs in **Step 2**. The correct coordinates after applying the 90° clockwise rotation should be \((-6, 5)\), not \((-6, -5)\).
1. **Step 1**: She states the rule for a 90° clockwise rotation as \((x, y) \rightarrow (y, -x)\). This is correct.
2. **Step 2**: She refers to switching the x and y coordinates. The original point M is \((-5, -6)\). According to the rotation rule, applying it should give:
\[
(x, y) = (-5, -6) \rightarrow (y, -x) = (-6, 5)
\]
However, Mira incorrectly states that this step results in \((-6, -5)\). This is where the first error occurs.
3. **Step 3**: Mira then states she multiplies the new x-coordinate by \(-1\), implying she was about to convert \(-6\) to \(6\). However, because she made an error in Step 2, her new x-coordinate is actually incorrect.
4. **Step 4**: Simplifying her erroneous coordinates \((6, -5)\) is also incorrect because she started with incorrect coordinates.
The error in Mira's solution occurs in **Step 2**. The correct coordinates after applying the 90° clockwise rotation should be \((-6, 5)\), not \((-6, -5)\).