#### 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 $P=\left(1;3\right)$ and $Q=\left(-1;7\right)$.
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 $P=\left(3;-1\right)$ and a radius of $r=\sqrt{10}$:
 The origin $\left(2;3\right)$ $\left(4;2\right)$ $\left(3;2\right)$ $\left(0;\sqrt{10}\right)$

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

$\left(x-2{\right)}^{2}+\left(y+3{\right)}^{2}\mathrm{ }=\mathrm{ }9 .$

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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