Chapter 9 Objects in the Two-Dimensional Coordinate System

Section 9.5 Final Test

9.5.1 Final Test Module 9

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Exercise 9.5.1
Specify the normal form of the equation of the line PQ that passes through the two points P=(1;3) and Q=(-1;7).  
Answer: y =

Exercise 9.5.2
Let a line be given by the equation 6x+2y=4.
  1. The normal form of this equation is y = .
  2. What is the relative position of this line with respect to the line described by the equation y=3x-2?
      There is no intersection point at all.
      There is exactly one intersection point.
      The lines coincide.

Exercise 9.5.3
Find the intersection point between the line described by the equation y=2x+2 and the line described by the equation 2x=6.  
Answer: The intersection point is .
Enter the points in the form (a;b).  
Tick the possible reasons why the equation of a line 2x=6 of the second line cannot be transformed into normal form. (Several statements can be true.)
  The equation of the line cannot be solved for x.
  The equation of the line cannot be solved for y.
  The equation of the line is not cancelled completely.
  The line is parallel to the x-axis.
  The line is parallel to the y-axis.
  The slope of the line is not finite.
  The line does not intersect the x-axis.

Exercise 9.5.4
Decide which of the following points lie on the circle with the centre P=(3;-1) and a radius of r=10:
  The origin

Exercise 9.5.5
Let a circle be defined by the following equation:

(x-2 )2 +(y+3 )2   =  9.

What are the properties of this circle?
  1. Its radius is r = .
  2. Its centre is M = .
    Enter points in the form (a;b).
  3. It intersects the line that passes though M and a second unknown point P
      at one point,
      at two points,
      at three points,
      not at all.


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