9000151301
Level:
B
Find the angle \(\varphi \)
between the lines \(3x - 7 = 0\)
and \(x + y + 13 = 0\).
\(45^{\circ }\)
\(90^{\circ }\)
\(60^{\circ }\)
\(30^{\circ }\)
Analytical Plane Geometry
9000151308
Level:
B
Given points \(A = [-1;4]\),
\(B = [2,-2]\) and
\(C = [5,-1]\), find the angle
\(\beta \) (the interior angle
at the vertex \(B\))
in the triangle \(ABC\).
\(98^{\circ }08'\)
\(81^{\circ }53'\)
\(76^{\circ }17'\)
\(68^{\circ }27'\)
9000151302
Level:
B
Find the angle \(\varphi \)
between the lines \(p\)
and \(q\)
given by their parametric equations.
\[
p\colon \begin{aligned}[t] x& = 1 + 2t, &
\\y& = 3 - 3t;\ t\in \mathbb{R},
\\ \end{aligned}\qquad q\colon \begin{aligned}[t] x& = 2 - k, &
\\y& = 3 + k;\ k\in \mathbb{R}
\\ \end{aligned}
\]
\(11^{\circ }19'\)
\(88^{\circ }41'\)
\(45^{\circ }45'\)
\(54^{\circ }12'\)
9000151304
Level:
B
Find the angle \(\varphi \)
between the lines \(y = 0\)
and \(\frac{x}
{2} + \frac{y}
{3} = 1\).
\(56^{\circ }19'\)
\(13^{\circ }45'\)
\(26^{\circ }46'\)
\(81^{\circ }23'\)
9000151309
Level:
B
Given points \(A = [-1.4]\),
\(B = [2,-2]\),
\(C = [5,-1]\), find the angle
\(\varphi \) between
the lines \(AB\)
and \(BC\).
\(81^{\circ }52'\)
\(98^{\circ }08'\)
\(61^{\circ }22'\)
\(45^{\circ }32'\)
9000151307
Level:
B
Find the angle \(\varphi \)
between the line \(x + \sqrt{3}y - 6 = 0\)
and the line \(p\)
given by it's parametric equations.
\[
p\colon \begin{aligned}[t] x& = 2 + t,&
\\y& = 5;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(30^{\circ }\)
\(90^{\circ }\)
\(60^{\circ }\)
\(45^{\circ }\)
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 \(p\).
\(8\)
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 \(p\) )
9000149404
Level:
B
Given points \(A = [-3;13]\),
\(K = [0;4]\),
\(L = [-5;-6]\), find the distance
from the point \(A\)
to the line \(KL\).
\(3\sqrt{5}\)
\(3\)
\(5\)
\(\sqrt{5}\)
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)