B

9000149409

Level: 
B
Find all lines which are parallel to \(p\colon x - 3y + 2 = 0\) and the distance from every of these lines to \(p\) is \(\sqrt{10}\).
\(p_{1}\colon x - 3y + 12 = 0\), \(p_{2}\colon x - 3y - 8 = 0\)
\(p\colon x - 3y = 0\)
\(p\colon x - 3y + \sqrt{10} = 0\)
\(p_{1}\colon x - 3y + \sqrt{10} = 0\), \(p_{2}\colon x - 3y -\sqrt{10} = 0\)

9000149406

Level: 
B
Given points \(A = [2;-5]\), \(B = [2;3]\) and \(C = [-4;-1]\), find the length of the altitude of the triangle \(ABC\) through the point \(C\). Hint: The altitude through the point \(C\) of a triangle \(ABC\) is the perpendicular line segment drawn from the vertex \(C\) to the line containing the side \(AB\).
\(6\)
\(\sqrt{2}\)
\(\frac{3} {2}\)
The points \(A\), \(B\), \(C\) do not define a triangle.

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.)