2010014412
Level:
A
Find the number \(c\) such that the point \(C=[5;c]\) lies on the line \(p\colon x=2+3t\), \(y=1+4t\), \(t \in \mathbb{R}\).
\(5\)
\(1\)
\(-1\)
\(2\)
Plane geometry
2010014413
Level:
A
Find the non-zero coordinate of the intersection point of the line \(p\colon -4x+3y-1=0\) and the \(x\)-axis.
\(-\frac14\)
\(5\)
\(-3\)
\(\frac13\)
2010014414
Level:
A
Find the non-zero coordinate of the intersection point of the line \(p\colon -x+y-1=0\) and the \(y\)-axis.
\(1\)
\(-1\)
\(0\)
\(2\)
2010014415
Level:
A
Find the parallel line to the line \(p\colon x-2y-3=0\), which goes through the point \(M=[1;1]\).
\(x-2y+1=0\)
\(2x-y-1=0\)
\(2x+y-3=0\)
\(2x-4y-3=0\)
2010014416
Level:
A
Find the perpendicular line to the line \(p\colon 3x-y+2=0\), which goes through the point \(M=[-1;1]\).
\(x+3y-2=0\)
\(x+3y+2=0\)
\(-x+3y-2=0\)
\(x-3y+1=0\)
2010014601
Level:
A
Find the normal vector of the line passing through the points
\(A = [1;3]\) and
\(B = [-2;5]\).
\((2;3)\)
\((-3;2)\)
\((3;-2)\)
\((2;-3)\)
2010014602
Level:
A
Find the normal vector of the following line.
\[
p\colon \begin{aligned}[t] x =&1 +4t, &
\\y =& - 3 -2t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\((1;2)\)
\((4;-2)\)
\((1;-3)\)
\((-2;1)\)
2010014603
Level:
A
In the following list identify a line which is perpendicular to the line
\( 2x +3y -7= 0\).
\(\begin{aligned}[t] x& = 2t, &
\\y & = -11+3t;\ t\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& = 1+3t, &
\\y & = 11 - 2t;\ t\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& = 2+t, &
\\y & = 3 - t;\ t\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& = 2t+7, &
\\y & = - 3t+1;\ t\in \mathbb{R}
\\ \end{aligned}\)
2010014604
Level:
A
Among the lines in the following list (slope-intercept form) identify a line perpendicular
to the line
\[
y = \frac{2}{3}x - 1.
\]
\(y = -\frac{3}
{2}x +1\)
\(y = \frac{2}
{3}x +1\)
\(y = \frac{3}
{2}x - 1\)
\(y = -\frac{1}
{2}x + 1\)
9000106001
Level:
A
In the following list identify a vector in the direction of the following parametric
line.
\[\begin{aligned}
x =\ &1 + t, & &
\\y =\ &3 + 2t;\ t\in \mathbb{R} & &
\end{aligned}\]
\(\left (1;2\right )\)
\(\left (1;3\right )\)
\(\left (0;2\right )\)
\(\left (3;1\right )\)