9000149402
Level:
B
Find the distance from the origin (i.e. the point
\([0.0]\)) to the
line \(p\colon x + 2y + 5 = 0\).
\(\sqrt{5}\)
\(1\)
The origin is on the line \(p\).
\(8\)
B
9000149306
Level:
B
Given a translation of a plane, find the property of a line obtained by translating a line
\(r\). The
line \(r\) is
neither parallel not perpendicular to the translation vector.
The resulting line is parallel to the line
\(r\).
The resulting line is perpendicular to the translation vector.
The resulting line is perpendicular to the line
\(r\).
The resulting line is the line \(r\).
(The line \(r\)
is mapped into itself.)
9000149403
Level:
B
Find the distance from the point \(M = [1;1]\)
to the line \(p\).
\[
\begin{aligned}p\colon x& = 3 + t, &
\\y & = 1 + t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(\sqrt{2}\)
\(2\)
\(1\)
\(0\) (the point is
on the line \(p\) )
9000149307
Level:
B
The rotation through an angle \(\alpha = 180^{\circ }\)
is equivalent to some other geometric mapping. Which one?
reflection through the point
reflection through the line
translation
9000149404
Level:
B
Given points \(A = [-3;13]\),
\(K = [0;4]\),
\(L = [-5;-6]\), find the distance
from the point \(A\)
to the line \(KL\).
\(3\sqrt{5}\)
\(3\)
\(5\)
\(\sqrt{5}\)
9000149308
Level:
B
Consider a rotation through an angle either
\(\alpha = 180^{\circ }\) or
\(\alpha = 360^{\circ }\). How
many lines which are mapped into itself exists for this rotation?
infinitely many
none
one
two
9000149407
Level:
B
Find the distance between the lines \(p\colon 3x - 4y + 1 = 0\)
and \(q\colon 3x - 4y + 4 = 0\).
\(\frac{3}
{5}\)
\(1\)
\(4\)
\(0\) (the
lines have an intersection)
9000149410
Level:
B
Find all lines passing through the point
\(A = [-2;-6]\) such that the distance
from the point \([0.0]\)
to these lines is \(2\sqrt{2}\).
\(p_{1}\colon 7x + y + 20 = 0\),
\(p_{2}\colon x - y - 4 = 0\)
\(p\colon 7x - y = 0\)
\(p\colon x + y + 2\sqrt{2} = 0\)
\(p_{1}\colon x - y + 2\sqrt{2} = 0\),
\(p_{2}\colon x + y - 2\sqrt{2} = 0\)
9000149706
Level:
B
Find the center of the following hyperbola.
\[
4x^{2} - 3y^{2} + 8x - 30y - 49 = 0
\]
\([-1;-5]\)
\([-1;5]\)
\([1;-5]\)
\([1;5]\)
9000149707
Level:
B
Find the center of the following hyperbola.
\[
5x^{2} - 6y^{2} - 30x + 12y + 9 = 0
\]
\([3;1]\)
\([3;-1]\)
\([-3;1]\)
\([-3;-1]\)