Question

Consider a polygonal f: R → R, formed by 8 segments with vertices (Vi; Wi), 1 ≤ i ≤ 7. What metric relations between the coordinates of these vertices must occur and what characteristics must the rays of the extremes satisfy to guarantee that this Is polygonal the result of a combination of translations and modules applied to a linear function?

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Answer to a math question Consider a polygonal f: R → R, formed by 8 segments with vertices (Vi; Wi), 1 ≤ i ≤ 7. What metric relations between the coordinates of these vertices must occur and what characteristics must the rays of the extremes satisfy to guarantee that this Is polygonal the result of a combination of translations and modules applied to a linear function?

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Sigrid
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Para que a poligonal seja resultado de uma combinação de translações e módulos aplicados sobre uma função linear, temos que as relações métricas entre as coordenadas dos vértices devem seguir um padrão específico.

Denotamos as coordenadas dos vértices da poligonal como (Vi, Wi), onde i assume valores de 1 a 7. Se uma poligonal é resultado de translações e módulos aplicados sobre uma função linear, as coordenadas dos vértices devem satisfazer as seguintes condições:

1. Movimento Linear: os vértices estão em uma reta. As coordenadas dos vértices formam uma progressão aritmética. Assim, temos que Wi = a + bVi, onde a e b são constantes reais.

2. Módulo: as distâncias entre os vértices são constantes. Portanto, a diferença entre as coordenadas consecutivas deve ser constante, ou seja, para todo i temos que Wi+1 - Wi = constante.

3. Semirretas dos Extremos: as semirretas que partem dos extremos da poligonal têm que ser paralelas. Ou seja, as retas definidas pelos segmentos (V1, W1) e (V7, W7) devem ser paralelas.

Tomando essas condições em consideração, temos que as relações métricas entre as coordenadas dos vértices da poligonal devem seguir o padrão de movimento linear, módulo e paralelismo das semirretas dos extremos.

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