9000107503
Level:
A
Among the lines in the following list (slope-intercept form) identify a line perpendicular
to the line
\[
y = \frac{3}{4}x + 1.
\]
\(y = -\frac{4}
{3}x - 2\)
\(y = -\frac{3}
{4}x - 1\)
\(y = \frac{4}
{3}x - 5\)
\(y = 3\)
Analytical Plane Geometry
9000106805
Level:
C
Given points \(A = [0;5]\),
\(B = [6;1]\),
\(C = [7;9]\),
find the direction vector of the line passing through the point
\(A\) and the midpoint of
the segment \(BC\) (i.e. the
median of the triangle \(ABC\)
through the vertex \(A\)).
\((1;0)\)
\((1;8)\)
\((1;9)\)
\((6.5;5)\)
9000107502
Level:
A
In the following list identify a line which is perpendicular to the line
\(q\).
\[
\begin{aligned}q\colon x& = 5 - t,&
\\y & = 3t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(p\colon x - 3y - 7 = 0\)
\(p\colon - x - 3y + 11 = 0\)
\(p\colon 3x - y = 0\)
\(p\colon y = 5\)
9000106201
Level:
A
In the following list identify a vector having the same direction as the parametric
line \(p\).
\[ \begin{alignedat}{80}
p\colon x & = 1 + 2t, & &\phantom{t\in \mathbb{R}} & & & &
\\y & = 3 - 4t;\ & &t\in \mathbb{R} & & & &
\\\end{alignedat}\]
\((1;-2)\)
\((1;3)\)
\((3;1)\)
\((2;3)\)
9000106202
Level:
A
In the following list identify a vector having the same direction as the parametric
line \(p\).
\[ \begin{aligned}
x & = 1 - t, \\
y & = t;\ t\in \mathbb{R}
\\\end{aligned}\]
\((1;-1)\)
\((0;0)\)
\((1;0)\)
\((1;1)\)
9000106203
Level:
A
In the following list identify a vector having the same direction as the parametric
line \(p\).
\[ \begin{aligned}
p\colon x & = -5, \\
y & = 5t;\ t\in \mathbb{R}
\end{aligned}\]
\((0;1)\)
\((5;5)\)
\((5;0)\)
\((-5;5)\)
9000106204
Level:
A
In the following list identify a vector having the same direction as the parametric
line \(p\).
\[ \begin{aligned}
x & = 2t, \\
y & = 0;\ t\in \mathbb{R}.
\\\end{aligned}\]
\((1;0)\)
\((0;0)\)
\((0;1)\)
\((0;2)\)
9000106207
Level:
A
In the following list identify a normal vector to the line
\(p\).
\[
p\colon - x + 2y + 3 = 0
\]
\((1;-2)\)
\((2;3)\)
\((-1;3)\)
\((2;-1)\)
9000106208
Level:
A
In the following list identify a normal vector to the line
\(p\).
\[
p\colon 2y - 1 = 0
\]
\((0;1)\)
\((2;0)\)
\((2;-1)\)
$(2;1)$
9000106801
Level:
A
Find the vector in the direction of the following line.
\[
2x + 1 = 3y - 2
\]
\((3;2)\)
\((-3;2)\)
\((2;-3)\)
\((-3;3)\)