Symmetry and Geometric Transformations

Project ID: 
6000000038
Accepted: 
Type: 
Layout: 
Question: 
In the diagram below, under which transformation will the triangle $A'B'C'$ be the image of the triangle $ABC$?
Question 1: 
{\obrA}
Question 1 Image: 
Answer 1: 

The reflection across the point $T$.

Question 2: 
{\obrB}
Question 2 Image: 
Answer 2: 

The line reflection across the line $TS$.

Question 3: 
{\obrC}
Question 3 Image: 
Answer 3: 

The rotation $45^{\circ}$ anticlockwise about the center $T$.

Question 4: 
{\obrD}
Question 4 Image: 
Answer 4: 

The translation by vector $\overset{\longrightarrow}{TS}$.

Answer 5: 

<p>The rotation $45^{\circ}$ clockwise about the center $T$.</p>

Answer 6: 

The reflection across the point $B$.

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; } }