Question

mira uses the mapping rule to find the coordinate of a point that had been rotated 90° clockwise about the origin. examine miras solution to determine which step has an error. m(-5, -6) is rotated 90° clockwise. miras work step 1. use the rule (x, y)→(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

Explanation:

Step1: Analyze the rotation rule

The rule for a \(90^{\circ}\) clockwise rotation about the origin is \((x,y)\to(y, -x)\). For the point \(M(-5,-6)\), applying the rule: \(x=-5\), \(y = -6\). The new coordinates should be \((-6,5)\) (since \(y=-6\) and \(-x=-(-5) = 5\)).

Step2: Check each step

• Step 1: Using the rule \((x,y)\to(y,-x)\) is correct.
• Step 2: Switching \(x\) and \(y\) coordinates: \((-5,-6)\) after switching \(x\) and \(y\) gives \((-6,-5)\). This is wrong. The correct switch (based on the rule \((x,y)\to(y,-x)\)) should be \((-6,5)\) (because \(-x=-(-5) = 5\)).
• Step 3: Since step 2 is wrong, step 3 (multiplying the new \(x\) - coordinate by \(-1\)) is also wrong. But the error originated in step 2.
• Step 4: Since step 2 is wrong, step 4 (simplifying) is also wrong. But the error originated in step 2.

Answer:

Step 2