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Abstract Algebra : Geometric Fields

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Example Questions

Example Question #1 : Geometric Fields

Identify the following definition.

For some subfield of $\mathbb{R}$ $\displaystyle \mathbb{R}$, in the Euclidean plane $\mathbb{R}^2$ $\displaystyle \mathbb{R}^2$, the set of all points (x,y) $\displaystyle (x,y)$ that belong to that said subfield is called the __________.

Possible Answers:

Angle

Line

Plane

None of the answers.

Constructible Line

Correct answer:

Plane

Explanation:

By definition, when $\displaystyle A$ is a subfield of $\mathbb{R}$ $\displaystyle \mathbb{R}$, in the Euclidean plane $\mathbb{R}^2$ $\displaystyle \mathbb{R}^2$, the set of all points (x,y) $\displaystyle (x,y)$ that belong to $\displaystyle A$ is called the plane of $\displaystyle A$.

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Example Question #2 : Geometric Fields

Identify the following definition.

Given that $\displaystyle A$ lives in the Euclidean plane $\mathbb{R}^2$ $\displaystyle \mathbb{R}^2$. Elements $\displaystyle a$, $\displaystyle b$, and $\displaystyle c$ in the subfield $\displaystyle A$ that form a straight line who's equation form is $\displaystyle ax+by+c=0$, is known as a__________.

Possible Answers:

Subfield

Circle in $\displaystyle A$

Plane

Line in $\displaystyle A$

Angle

Correct answer:

Line in $\displaystyle A$

Explanation:

By definition, given that $\displaystyle A$ lives in the Euclidean plane $\mathbb{R}^2$ $\displaystyle \mathbb{R}^2$. When elements $\displaystyle a$, $\displaystyle b$, and $\displaystyle c$ in the subfield $\displaystyle A$ , form a straight line who's equation form is $\displaystyle ax+by+c=0$, is known as a line in $\displaystyle A$.

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Example Question #3 : Geometric Fields

Identify the following definition.

Possible Answers:

Subfield

Circle in $\displaystyle A$

Angle

Plane

Line in $\displaystyle A$

Correct answer:

Line in $\displaystyle A$

Explanation:

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Example Question #4 : Geometric Fields

Identify the following definition.

If a line segment has length |a| $\displaystyle |a|$ and is constructed using a straightedge and compass, then the real number $\displaystyle a$ is a __________.

Possible Answers:

Angle

Plane

Magnitude

Straight Line

Constructible Number

Correct answer:

Constructible Number

Explanation:

By definition if a line segment has length |a| $\displaystyle |a|$ and it is constructed using a straightedge and compass then the real number $\displaystyle a$ is a known as a constructible number.

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Abstract Algebra : Geometric Fields

Study concepts, example questions & explanations for Abstract Algebra

All Abstract Algebra Resources

Example Questions

Example Question #1 : Geometric Fields

Example Question #2 : Geometric Fields

Example Question #3 : Geometric Fields

Example Question #4 : Geometric Fields

All Abstract Algebra Resources

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