Parametric Equations of a Line and of Objects on a Line

Submitted by ladislav.foltyn on Thu, 05/02/2019 - 14:40
Project ID: 
5000000055
Accepted: 
SubArea: 
Plane geometry
Template: 
B
Question: 
\vspace*{-1em} We are given points A=[−1;3] and B=[3;6]. Further, we are given parametric equations of a straight line AB: x=−1+4t, y=3+3t; t∈R. Match each described object lying on the straight line AB with the corresponding set of values of parameter t. \vspace*{-1em}
Question Row 1: 
\ifen Centre of the line segment AB \fi \ifcs Střed úsečky AB \fi \ifpl Środek odcinka prostej AB \fi \ifsk Stred úsečky AB \fi \ifes El centro del segmento AB \fi
Answer Row 1: 
t∈{2}, t∈{−12}, *t∈{12}, t∈{−2}
Question Row 2: 
\ifen The line segment AB \fi \ifcs Úsečka AB \fi \ifpl Odcinek prostej AB \fi \ifsk Úsečka AB \fi \ifes El segmento AB \fi
Answer Row 2: 
t∈{0;1}, t∈⟨−1;0⟩, t∈⟨−1;1⟩, *t∈⟨0;1⟩
Question Row 3: 
\ifen The ray AB \fi \ifcs Polopřímka AB \fi \ifpl Półprosta AB \fi \ifsk Polpriamka AB \fi \ifes La semirrecta AB \fi
Answer Row 3: 
t∈(0;∞), t∈⟨−∞;0), *t∈⟨0;∞), t∈⟨1;∞)
Question Row 4: 
\ifen The ray BA \fi \ifcs Polopřímka BA \fi \ifpl Półprosta BA \fi \ifsk Polpriamka BA \fi \ifes La semirrecta BA \fi
Answer Row 4: 
*t∈(−∞;1⟩, t∈⟨−∞;0), t∈⟨−∞;1), t∈⟨−1;∞)
Question Row 5: 
\ifen The point of intersection of the line AB with x-axis \fi \ifcs Průsečík přímky AB s osou x \fi \ifpl Punkt przecięcia prostej AB z osią x \fi \ifsk Priesečník priamky AB s osou x \fi \ifes El punto de intersección de la recta AB con el eje x \fi
Answer Row 5: 
t∈{−5}, *t∈{−1}, t∈{0}, t∈{14}
Question Row 6: 
\ifen The point of intersection of the line AB with y-axis \fi \ifcs Průsečík přímky AB s osou y \fi \ifpl Punkt przecięcia prostej AB z osią y \fi \ifsk Priesečník priamky AB s osou y \fi \ifes El punto de intersección de la recta AB con el eje y \fi
Answer Row 6: 
t∈{−13}, *t∈{14}, t∈{154}, t∈{0}
Question Row 7: 
\ifen The point $M\in AB;$ $M=[?;4]$ \fi \ifcs Bod $M\in AB;$ $M=[?;4]$ \fi \ifpl Punkt $M\in AB;$ $M=[?;4]$ \fi \ifsk Bod $M\in AB;$ $M=[?;4]$ \fi \ifes El punto $M\in AB;$ $M=[?;4]$ \fi
Answer Row 7: 
t∈{14}, t∈{1}, *t∈{13}, t∈{−1}
Question Row 8: 
\ifen The point N∈AB; N=[2;?] \fi \ifcs Bod N∈AB; N=[2;?] \fi \ifpl Punkt N∈AB; N=[2;?] \fi \ifsk Bod N∈AB; N=[2;?] \fi \ifes El punto N∈AB; N=[2;?] \fi
Answer Row 8: 
*t∈{34}, t∈{1}, t∈{13}, t∈{14}
Tex: 
% tiket 32955 \MsrTabulka[1pt]{0.23\linewidth}{0.7\linewidth} \pocetsloupcu{4}