30 points and brainliest for the correct answers.

As we know that a line is a set of points which tend to extend infinitely in two directions.
So, in question 1, two points C and D are shown on a line. As a line carries these two points - the infinite line that includes C and D. Double arrow indicates that line is extended infinitely in both directions. While the order of the points does not matter for a line, it is conventional to name the two points in alphabetical order. So, the figure is named as a line 'CD'. So, option B is correct.

Note: The symbol '⟷' is placed UPPER on a line 'CD'. Also remember, that the a line is named in alphabetical order.

Question # 2

Which of the following correctly names a line shown in the figure?

Answer:

The option A is correct as the line AP carries the points A and P and extends infinitely in two directions, and the symbol '⟷' is placed UPPER on a line 'AP' which represents the line.

Explanation:

Let us look at some definitions.

Point - has no length, no width, and no height, but it carries a location.
Line - a set of points which tend to extend infinitely in two directions. For example line AB.
Line Segment - is a piece of line having two end points. For example, segment [tex]{\overline {AB}}[/tex].
Ray - a part of line with one end point. For example, Ray [tex]{\overrightarrow {AB}}[/tex]

As we have to determine the correct name of a line shown in figure in question 2. So, we need to recall that a line is a set of points which tend to extend infinitely in two directions. Double arrow indicates that line is extended infinitely in both directions.

In question 2, the figure shows that:

[tex]{\overrightarrow {EC}}[/tex] is a ray as it is a part of line with one end point, heading towards infinity in only one direction. Hence, option B is also not a line.
[tex]{\overline {NH}}[/tex] is a line segment because it has two end points. Hence, option C is not a line.
Option D can not be correct as the symbol ' [tex]{\overline {~~}}[/tex] 'is placed upper on AP. This symbol represents the segment.
As we know that a line is a set of points which tend to extend infinitely in two directions. Double arrow indicates that line is extended infinitely in both directions. The symbol '⟷' is placed UPPER on a line 'AP'. Hence, the option A is correct as the line AP carries the points A and P, and the symbol '⟷' is placed UPPER on a line 'AP' which represents the line.

So, option A is correct.

Question 3.

Which of the following correctly names a ray shown in the figure?

Answer:

option B is correct. i.e. [tex]{\overrightarrow {EG}}[/tex] correctly names a ray.

Explanation:

The option A can not be correct as the symbol ' [tex]{\overline {~~}}[/tex] 'is placed upper on EP. This symbol represents the segment as EP is a line segment.

The option C cannot be true as the '⟷' is placed UPPER on 'LG' which represents the line.

The option D cannot be true also as it is showing the wrong end point of a ray. As the actual ray would have had E as the end point, and directed towards C, and would have mentioned as [tex]{\overrightarrow {CE}}[/tex]. But, the option D is wrongly mentioning as [tex]{\overrightarrow {EC}}[/tex].
As we know that a ray is a part of line with one end point. If we carefully observe the figure, only option B i.e. [tex]{\overrightarrow {EG}}[/tex] is correct. As E is the end point, and directed towards G. So, it becomes [tex]{\overrightarrow {EG}}[/tex]. We cannot call it [tex]{\overrightarrow {GE}}[/tex] as G is not the end point. An array has only one arrow. So, option B is correct.

Keywords: ray, segment, line

Learn more about rays, lines, and segments from brainly.com/question/909890

#learnwithBrainly