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.
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.)
Find the distance from the point \(M = [1;1]\)
to the line \(p\).
\[
\begin{aligned}p\colon x& = 3 + t, &
\\y & = 1 + t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
Let \(A\) be a
set with \(n\)
mutually different elements. If we add one element to the set
\(A\), the number of
\(3\)-combinations
of a set \(A\) is
increased by \(21\).
Find \(n\).