#### Chapter 9 Objects in the Two-Dimensional Coordinate System

**Section 9.5 Final Test**

# 9.5.1 Final Test Module 9

This is a test for submission:- Unlike open exercises, no hints for formulating mathematical expressions are provided.

- The test can be restarted or interrupted at any time.

- The test can be terminated and submitted using the buttons at the end of the page, or reset.

- The test can be attempted several times. Only the last version will be included in the statistics.

##### **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$$\hspace{0.5em}=\hspace{0.5em}$

.

Answer: $y$$\hspace{0.5em}=\hspace{0.5em}$

.

##### **Exercise 9.5.2 **

Let a line be given by the equation $6x+2y=4$.

- The normal form of this equation is $y$$\hspace{0.5em}=\hspace{0.5em}$ .

- 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

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.)

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 $r=\sqrt{10}$:

The origin | ||

$(2;3)$ | ||

$(4;2)$ | ||

$(3;2)$ | ||

$(0;\sqrt{10})$ |

##### **Exercise 9.5.5 **

Let a circle be defined by the following equation:

$(x-2{)}^{2}+(y+3{)}^{2}\mathrm{\hspace{0.5em}\hspace{0.5em}}=\mathrm{\hspace{0.5em}\hspace{0.5em}}9\hspace{0.5em}.$

What are the properties of this circle?

What are the properties of this circle?

- Its radius is $r$$\hspace{0.5em}=\hspace{0.5em}$ .

- Its centre is $M$$\hspace{0.5em}=\hspace{0.5em}$ .

Enter points in the form`(a;b)`.

- 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.

The test evaluation will be displayed here!