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: \(x=-5\), \(y = -6\), so the new coordinates should be \((-6,5)\) (since \((-5,-6)\to(-6, -(-5))=(-6,5)\)).

Step2: Check Mira's steps

• Step 1: Using the rule \((x,y)\to(y,-x)\) is correct.
• Step 2: Switching \(x\) and \(y\) coordinates: for \(M(-5,-6)\), after switching \(x\) and \(y\) we get \((-6,-5)\). But according to the rule, the \(x\) - coordinate of the image is \(y=-6\) and the \(y\) - coordinate of the image is \(-x=-(-5) = 5\). So Step 2 is wrong. Mira just switched \(x\) and \(y\) without changing the sign of the new \(y\) - coordinate as per the rule.

Answer:

\(2\)