Project ID:
6000000066
Accepted:
Tipo:
Layout:
Question:
Una recta $p$ viene definida por un punto $A$ y su ángulo de inclinación $\varphi$. Para cada recta, elige su correcta ecuación en forma punto-pendiente.
Questions Title:
Gráficas:
Answers Title:
Ecuaciones:
Question 1:
{\obrA}
Question 1 Image:
Answer 1:
$p\colon y=-\sqrt3x+3$
Question 2:
{\obrB}
Question 2 Image:
Answer 2:
$p\colon y=\frac{\sqrt3}3x+3$
Question 3:
{\obrC}
Question 3 Image:
Answer 3:
$p\colon y=\sqrt3x+3$
Question 4:
{\obrD}
Question 4 Image:
Answer 4:
$p\colon y=-x+3$
Question 5:
{\obrE}
Question 5 Image:
Answer 5:
$p\colon y=x+3$
Question 6:
{\obrF}
Question 6 Image:
Answer 6:
$p\colon -\frac{\sqrt3}3x+3$
Answer 7:
$p\colon y=-2x+3$
Answer 8:
$p\colon y=2x+3$
Tex:
% tiket 32953
\NastavOD{4}
\def\obrA{\obrMsr[x=0.5cm,y=0.5cm]{-3}{6}{-2}{6}
{
\footnotesize
\coordinate (A) at (0,3);
\coordinate (B) at ({3/3^(1/2)},0);
\coordinate (C) at (6,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2,4}
\obrPopisY[left]{2,4}
\obrZnackyX{-1,1,3,5}
\obrZnackyY{-1,1,3,5}
\obrFce{-3^(1/2)*(\x)+3}
\draw[red] (-1,{3^(1/2)+3}) node [below left]{$p$};
\begin{scope}[thick]
\obrKrizek[2pt] {A}{above right}{A=[0;3]}
\end{scope}
\obrUhelB*[1.5cm] ABC
\obrUhelBZnacka[xshift=10pt,yshift=6pt] {A}{B}{C}{$\varphi=120^{\circ}$}
}}
\def\obrB{\obrMsr[x=0.5cm,y=0.5cm]{-7}{3}{-2}{6}
{
\footnotesize
\coordinate (A) at (0,3);
\coordinate (B) at ({-9/3^(1/2)},0);
\coordinate (C) at (6,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-6,-4,-2,2}
\obrPopisY[left]{2,4}
\obrZnackyX{-5,-3,-1,1}
\obrZnackyY{-1,1,3,5}
\obrFce{3^(1/2)/3*(\x)+3}
\draw[red] (-1,{-3^(1/2)/3+3}) node [above left]{$p$};
\begin{scope}[thick]
\obrKrizek[2pt] {A}{below right}{A=[0;3]}
\end{scope}
\obrUhelB*[2cm] ABC
\obrUhelBZnacka[xshift=25pt,yshift=6pt] {A}{B}{C}{$\varphi=30^{\circ}$}
}}
\def\obrC{\obrMsr[x=0.5cm,y=0.5cm]{-4}{5}{-2}{6}
{
\footnotesize
\coordinate (A) at (0,3);
\coordinate (B) at ({-3/3^(1/2)},0);
\coordinate (C) at (6,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2,4}
\obrPopisY[left]{2,4}
\obrZnackyX{-3,-1,1,3}
\obrZnackyY{-1,1,3,5}
\obrFce{3^(1/2)*(\x)+3}
\draw[red] (1.5,{1.5*3^(1/2)+3}) node [below right]{$p$};
\begin{scope}[thick]
\obrKrizek[2pt] {A}{left}{A=[0;3]}
\end{scope}
\obrUhelB*[1.75cm] ABC
\obrUhelBZnacka[xshift=18pt,yshift=4pt] {A}{B}{C}{$\varphi=60^{\circ}$}
}}
\def\obrD{\obrMsr[x=0.5cm,y=0.5cm]{-3}{7}{-2}{6}
{
\footnotesize
\coordinate (A) at (0,3);
\coordinate (B) at ({3},0);
\coordinate (C) at (6,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2,4,6}
\obrPopisY[left]{2,4}
\obrZnackyX{-1,1,3,5}
\obrZnackyY{-1,1,3,5}
\obrFce{-(\x)+3}
\draw[red] (-2,{2+3}) node [below left]{$p$};
\begin{scope}[thick]
\obrKrizek[2pt] {A}{above right}{A=[0;3]}
\end{scope}
\obrUhelB*[1.5cm] ABC
\obrUhelBZnacka[xshift=8pt,yshift=6pt] {A}{B}{C}{$\varphi=135^{\circ}$}
}}
\def\obrE{\obrMsr[x=0.5cm,y=0.5cm]{-5}{5}{-2}{6}
{
\footnotesize
\coordinate (A) at (0,3);
\coordinate (B) at (-3,0);
\coordinate (C) at (6,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-4,-2,2,4}
\obrPopisY[left]{2,4}
\obrZnackyX{-3,-1,1,3}
\obrZnackyY{-1,1,3,5}
\obrFce{(\x)+3}
\draw[red] (2,{2+3}) node [below right]{$p$};
\begin{scope}[thick]
\obrKrizek[2pt] {A}{below right}{A=[0;3]}
\end{scope}
\obrUhelB*[1.75cm] ABC
\obrUhelBZnacka[xshift=15pt,yshift=4pt] {A}{B}{C}{$\varphi=45^{\circ}$}
}}
\def\obrF{\obrMsr[x=0.5cm,y=0.5cm]{-2}{10}{-2}{6}
{
\footnotesize
\coordinate (A) at (0,3);
\coordinate (B) at ({9/3^(1/2)},0);
\coordinate (C) at (6,0);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{2,4,6,8}
\obrPopisY[left]{2,4}
\obrZnackyX{-3,-1,1,3,5,7,9}
\obrZnackyY{-1,1,3,5}
\obrFce{-3^(1/2)/3*(\x)+3}
\draw[red] (-1.5,{3^(1/2)/3*1.5+3}) node [above right]{$p$};
\begin{scope}[thick]
\obrKrizek[2pt] {A}{above right}{A=[0;3]}
\end{scope}
\obrUhelB*[1.5cm] ABC
\obrUhelBZnacka[xshift=3pt,yshift=9pt] {A}{B}{C}{$\varphi=150^{\circ}$}
}}