Plane geometry

2010014608

Level: 
B
Find a general form equation of the straight line that passes through the point \( M=[2;-3] \) and is parallel with the line of symmetry of the line segment \( AB \), where \( A=[4;-1] \), and \( B=\left[-3;\frac32\right] \) (see the picture).
\( 14x-5y-43=0 \)
\( 5x-14y-52=0 \)
\( 14x+5y-13=0 \)
\( 5x+14+32=0 \)

2010014607

Level: 
B
Given points \(A = [3;3]\), \(B = [-5;3]\) and \(C = [-1;-1]\), 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 \(AB\).
\(4\)
\(\frac43\)
\(6\)
\(\frac23\)

2010014603

Level: 
A
In the following list identify a line which is perpendicular to the line \( 2x +3y -7= 0\).
\(\begin{aligned}[t] x& = 2t, & \\y & = -11+3t;\ t\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] x& = 1+3t, & \\y & = 11 - 2t;\ t\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] x& = 2+t, & \\y & = 3 - t;\ t\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] x& = 2t+7, & \\y & = - 3t+1;\ t\in \mathbb{R} \\ \end{aligned}\)