Project ID:
6000000038
Accepted:
Typ:
Layout:
Question:
Spójrz na diagram, jakiego przekształcenia należy użyć, aby trójkąt $A'B'C'$ był obrazem trójkąta $ABC$?
Question 1:
{\obrA}
Question 1 Image:
Answer 1:
Symetria środkowa względem punktu $T$.
Question 2:
{\obrB}
Question 2 Image:
Answer 2:
Symetria osiowa względem prostej $TS$.
Question 3:
{\obrC}
Question 3 Image:
Answer 3:
Obrót o $45^{\circ}$ przeciwnie do ruchu wskazówek zegara względem środka $T$.
Question 4:
{\obrD}
Question 4 Image:
Answer 4:
Przesunięcie o wektor $\overset{\longrightarrow}{TS}$.
Answer 5:
Obrót o $45^{\circ}$ zgodnie z ruchem wskazówek zegara względem środka $T$.
Answer 6:
Symetria środkowa względem punktu $B$.
Tex:
% tiket 32859
\usetikzlibrary{arrows,decorations.markings}
\NastavOD{2}
\def\obrA{
\obrMsr[x=0.6cm,y=0.6cm]{-1}2{-1}2
{
\footnotesize
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at (3.5,4);
\coordinate (T) at (5,1);
\coordinate (A1) at (10,2);
\coordinate (B1) at (6,2);
\coordinate (C1) at (6.5,-2);
\draw[dashdotted] (A) -- (A1);
\draw[dashdotted] (B) -- (B1);
\draw[dashdotted] (C) -- (C1);
\begin{scope}[thick]
\obrKrizek[2pt]{T}{above, yshift=4pt, xshift=2pt}{T}
\end{scope}
\draw[thick] (A) node [below]{$A$} -- (B) node [below]{$B$} -- (C) node [above]{$C$} -- cycle;
\draw[thick, red] (A1) node [above]{$A'$} -- (B1) node [above]{$B'$} -- (C1) node [below]{$C'$} -- cycle;
}
}
\def\obrB{
\obrMsr[x=0.4cm,y=0.4cm]{-1}2{-1}2
{
\footnotesize
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at (3.5,4);
\coordinate (T) at (3,-4);
\coordinate (S) at (7,4);
\coordinate (A1) at (8,-4);
\coordinate (B1) at (5.6,-0.8);
\coordinate (C1) at (9.1,1.2);
\draw[dashdotted] (A) -- (A1);
\draw[dashdotted] (B) -- (B1);
\draw[dashdotted] (C) -- (C1);
\draw[thick] (2,-6) -- (8,6);
\begin{scope}[thick]
\obrKrizek[2pt]{T}{below right}{T}
\obrKrizek[2pt]{S}{below right}{S}
\end{scope}
\draw[thick] (A) node [below]{$A$} -- (B) node [below]{$B$} -- (C) node [above]{$C$} -- cycle;
\draw[thick, red] (A1) node [below]{$A'$} -- (B1) node [below left]{$B'$} -- (C1) node [above right]{$C'$} -- cycle;
}
}
\def\obrC{
\obrMsr[x=0.7cm,y=0.7cm]{-1}2{-1}2
{
\footnotesize
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at (3.5,4);
\coordinate (T) at (2,2);
\coordinate (A1) at (2,-0.83);
\coordinate (B1) at (4.83,2);
\coordinate (C1) at (1.65,4.47);
\begin{scope}[thick]
\obrKrizek[2pt]{T}{below right}{T}
\end{scope}
\draw[thick] (A) node [below]{$A$} -- (B) node [below]{$B$} -- (C) node [above]{$C$} -- cycle;
\draw[thick, red] (A1) node [below]{$A'$} -- (B1) node [right]{$B'$} -- (C1) node [above]{$C'$} -- cycle;
}
}
\def\obrD{
\obrMsr[x=0.7cm,y=0.7cm]{-1}2{-1}2
{
\footnotesize
\coordinate (A) at (0,0);
\coordinate (B) at (4,0);
\coordinate (C) at (3.5,4);
\coordinate (T) at (2.5,1);
\coordinate (S) at (3.81,1.5);
\coordinate (A1) at (1.31,0.5);
\coordinate (B1) at (5.31,0.5);
\coordinate (C1) at (4.81,4.5);
\draw[thick,decoration={markings,mark=at position 1 with
{\arrow[scale=1,>=stealth]{latex}}},postaction={decorate}] (T) -- (S);
\begin{scope}[thick]
\obrKrizek[2pt]{T}{above}{T}
\obrKrizek[2pt]{S}{above right}{S}
\end{scope}
\draw[thick] (A) node [below]{$A$} -- (B) node [below]{$B$} -- (C) node [above]{$C$} -- cycle;
\draw[thick, red] (A1) node [left]{$A'$} -- (B1) node [right]{$B'$} -- (C1) node [above]{$C'$} -- cycle;
}
}