2010014406
Level:
A
Find the perpendicular line to the line \(p\colon x=1-2t\), \(y=-3+5t\), \(t \in \mathbb{R}\).
\(2x-5y+1=0\).
\(5x+2y-1=0\).
\(4x+10y+4=0\).
\(x-3y+2=0\).
Plane geometry
2010014405
Level:
A
Find the perpendicular line to the line \(p\colon x=1+5t\), \(y=-3-2t\), \(t \in \mathbb{R}\).
\(-5x+2y+1=0\)
\(2x+5y-3=0\)
\(-4x+10y-1=0\)
\(2x-5y-3=0\)
2010014404
Level:
A
Find the parallel line to the line \(p\colon -3x+y-5=0\).
\(6x-2y-5=0\)
\(x+3y-5=0\)
\(-6x-2y+1=0\)
\(-x-3y-1=0\)
2010014403
Level:
A
Find the parallel line to the line \(p\colon -x+3y-5=0\).
\(2x-6y-5=0\)
\(3x+y+2=0\)
\(-2x-6y+1=0\)
\(-x-3y-3=0\)
2010014402
Level:
A
Find the perpendicular line to the line \(2x-3y+1=0\).
\(3x+2y-4=0\)
\(4x-6y+2=0\)
\(3x-2y+1=0\)
\(-2x+3y-1=0\)
2010014401
Level:
A
Find the perpendicular line to the line \(3x-2y+1=0\).
\(2x+3y-4=0\)
\(6x-4y+2=0\)
\(2x-3y+1=0\)
\(-2x+3y-3=0\)
2010014210
Level:
A
In the following list find the vector having the same direction as the line
\(p\).
\[
p\colon 2x +3y + 1 = 0
\]
\(\left (-3;2\right )\)
\(\left (2;3\right )\)
\(\left (2;-3\right )\)
\(\left (3;1\right )\)
2010014209
Level:
A
In the following list identify a vector having the same direction as the line passing through
the points \(A\)
and \(B\).
\[
A = \left [4;1\right ],\ \qquad B = \left [3;2\right ]
\]
\(\left (-1;1\right )\)
\(\left (1;1\right )\)
\(\left (7;3\right )\)
\(\left (5;5\right )\)
2010014208
Level:
C
Given lines \(p\)
and \(q\), find
\(m\in \mathbb{R}\) such that
the lines \(p\)
and \(q\)
are parallel.
\[
p\colon x +3y + 4= 0,\qquad q\colon mx -2y - 7= 0
\]
\( m=-\frac23 \)
\( m=6 \)
\( m=-\frac13 \)
\( m=\frac13 \)
2010014207
Level:
C
Given two points \(A = [2;1]\)
and \(B = [4;-2]\), identify a
number \(m\in \mathbb{R}\) such
that the point \(C = [1;m]\)
is on the line \(AB\).
\( m=\frac52 \)
\( m=-\frac12 \)
\( m=2 \)
\( m=\frac13 \)