Question

quinton tried to transform triangle fgh according to the rule $(x,y)\to(-y,x)$. which best describes his attempt?
correct. he transformed the triangle according to the rule $(x,y)\to(-y,x)$.
incorrect. he transformed the triangle according to the rule $(x,y)\to(y,-x)$
incorrect. he transformed the triangle according to the rule $(x,y)\to(-y,-x)$
incorrect. he transformed the triangle according to the rule $(x,y)\to(-x,-y)$

Explanation:

Step1: Find coordinates of original triangle

Original points: \(F(4,2)\), \(G(1,2)\), \(H(4,5)\)

Step2: Apply the rule \((x,y)\to(-y,x)\)

For \(F(4,2)\): \((-2,4)\)
For \(G(1,2)\): \((-2,1)\)
For \(H(4,5)\): \((-5,4)\)

Step3: Find coordinates of transformed triangle

Transformed points: \(F'(-5,4)\), \(G'(-2,1)\), \(H'(-2,4)\)

Step4: Apply the rule \((x,y)\to(-y,-x)\)

For \(F(4,2)\): \((-2,-4)\) (not matching)
For \(G(1,2)\): \((-2,-1)\) (not matching)
For \(H(4,5)\): \((-5,-4)\) (not matching)

Step5: Apply the rule \((x,y)\to(y,-x)\)

For \(F(4,2)\): \((2,-4)\) (not matching)
For \(G(1,2)\): \((2,-1)\) (not matching)
For \(H(4,5)\): \((5,-4)\) (not matching)

Step6: Apply the rule \((x,y)\to(-x,-y)\)

For \(F(4,2)\): \((-4,-2)\) (not matching)
For \(G(1,2)\): \((-1,-2)\) (not matching)
For \(H(4,5)\): \((-4,-5)\) (not matching)

Answer:

Incorrect. He transformed the triangle according to the rule \((x,y)\to(-y,-x)\)