Analytical Plane Geometry

9000106806

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 perpendicular to the segment \(BC\) (i.e. the line which contains the altitude of the triangle \(ABC\) through the point \(A\)).
\((8;-1)\)
\((1;8)\)
\((1;9)\)
\((-9;1)\)

9000106807

Level: 
C
Consider the points \(A = [0;5]\), \(B = [6;1]\), \(C = [7;9]\) and the triangle \(ABC\). Find the direction vector of the line which is the perpendicular bisector of the side \(b\) (i.e. the line through the midpoint of the side \(AC\) which is perpendicular to the segment \(AC\)).
\((4;-7)\)
\((7;4)\)
\((7;9)\)
\((7;-9)\)

9000106001

Level: 
A
In the following list identify a vector in the direction of the following parametric line. \[\begin{aligned} x =\ &1 + t, & & \\y =\ &3 + 2t;\ t\in \mathbb{R} & & \end{aligned}\]
\(\left (1;2\right )\)
\(\left (1;3\right )\)
\(\left (0;2\right )\)
\(\left (3;1\right )\)

9000106002

Level: 
A
In the following list identify a vector in the direction of the following parametric line. \[\begin{aligned} x =\ &t - 1, & & \\y =\ &t - 2;\ t\in \mathbb{R}\text{.} & & \end{aligned}\]
\(\left (1;1\right )\)
\(\left (1;2\right )\)
\(\left (-1;-2\right )\)
\(\left (1;-1\right )\)

9000106006

Level: 
A
In the following list identify a vector having the same direction as the line passing through the points \(A\) and \(B\). \[ A = \left [-3;-1\right ]\text{, }\qquad B = \left [-1;-2\right ] \]
\(\left (2;-1\right )\)
\(\left (-4;-3\right )\)
\(\left (1;2\right )\)
\(\left (2;1\right )\)