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: Encontrar las coordenadas de los vértices

Coordenadas de \(F=(3,2)\), \(G=(1,2)\), \(H=(4,5)\)
Coordenadas de \(F'=(-2,3)\), \(G'=(-2,1)\), \(H'=(-5,4)\)

Step2: Aplicar la regla \((x,y)\to(-y,x)\)

Para \(F=(3,2)\): \((3,2)\to(-2,3)\)
Para \(G=(1,2)\): \((1,2)\to(-2,1)\)
Para \(H=(4,5)\): \((4,5)\to(-5,4)\)

Step3: Comprobar la regla aplicada por Quinton

Si la regla aplicada fuera \((x,y)\to(y, -x)\):
Para \(F=(3,2)\): \((3,2)\to(2,-3)
eq(-2,3)\)
Si la regla aplicada fuera \((x,y)\to(-y,-x)\):
Para \(F=(3,2)\): \((3,2)\to(-2,-3)
eq(-2,3)\)
Si la regla aplicada fuera \((x,y)\to(-x,-y)\):
Para \(F=(3,2)\): \((3,2)\to(-3,-2)
eq(-2,3)\)

Answer:

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