Analytic geometry in a plane
Parametric Equations for the Given Line Segment
Submitted by vladimir.arzt on Sun, 03/17/2024 - 14:01Equation of Straight Line
Submitted by vladimir.arzt on Fri, 03/15/2024 - 21:362010014610
Level:
B
Given points \(A = [4;-1]\),
\(B = [2,-3]\) and
\(C = [5,5]\), find the angle
\(\beta \) (the interior angle
at the vertex \(B\))
in the triangle \(ABC\).
\(24^{\circ }27'\)
\(144^{\circ }46'\)
\(155^{\circ }33'\)
\(11^{\circ }05'\)
2010014609
Level:
B
Find the angle \(\varphi \)
between the lines \(2x +1 = 0\)
and \(x - y + 7 = 0\).
\(45^{\circ }\)
\(60^{\circ }\)
\(90^{\circ }\)
\(30^{\circ }\)
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 \(AB\).
\(4\)
\(\frac43\)
\(6\)
\(\frac23\)
2010014606
Level:
B
Find all the values of the parameter \(c\) so that the distance from the point \(M = [1;-2]\)
to the line \(-4x + 3y + c = 0\) equals \(5\).
\(c\in \{ - 15;35\}\)
\(c\in \{ 15\}\)
\(c\in \{ 15;25\}\)
\(c\in \{ -5;5\}\)
2010014605
Level:
B
Find the distance from the point \(P = [2;4]\)
to the line \(4x - 3y - 5 = 0\).
\(\frac95\)
\(3\)
\(\frac45\)
The line contains \(P\).
2010014604
Level:
A
Among the lines in the following list (slope-intercept form) identify a line perpendicular
to the line
\[
y = \frac{2}{3}x - 1.
\]
\(y = -\frac{3}
{2}x +1\)
\(y = \frac{2}
{3}x +1\)
\(y = \frac{3}
{2}x - 1\)
\(y = -\frac{1}
{2}x + 1\)