Mathematics, 09.08.2021 21:30, TeEvalyn9623

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$\overleftrightarrow{AB}$ can be named in another way as $\overleftrightarrow{AC}$ Two other names for plane Q would be AEC and CDBEBD is not an acceptable name for plane Q because the points E, B and D are collinear

Given: Figure of a plane named Q with a normal $\overleftrightarrow{BF}$ at point B, containing two lines $\overleftrightarrow{AC}$ and $\overleftrightarrow{DE}$ that intersect at point B

To find:

Another name for $\overleftrightarrow{AB}$ Two other names for plane QWhy EBD is not an acceptable name for plane Q

A line is named using any two points lying on it. A plane, on the other hand is named using any three non-collinear points lying on it.

The logic behind this is that there is an unique line passing through any two points. So, any two points lying on a line is sufficient to name the line.

Similarly, an unique plane can be found that passes through any two lines. That is, any two lines lying on a plane is sufficient to name the plane. Since a line can be defined uniquely by two points, two lines can be defined uniquely by two points each, that is, four points. However, if we take a common point, that is, if we take the point of intersection of the two lines as one of our points, then we need at most three points to define a plane.

Note that, we have to take care that the three points be non-collinear, because if they are collinear, they can only give a single unique line which is not sufficient to uniquely give a plane. Indeed, infinite number of planes passes through a single line.

So, we name a line using two points lying on it and a plane using three non-collinear points lying on it.

Now, the line $\overleftrightarrow{AB}$ clearly passes through points A and B. As can be seen from the figure, it also passes through the point C. We name a line using any two points lying on the line.

So, another name for $\overleftrightarrow{AB}$ can be $\overleftrightarrow{AC}$ .

The plane Q contains the points A, B, C, D and E of which the points A, B and C, and the points E, B and D are collinear. So, choosing two sets of three points each such that they are non-collinear, we can have points A, E and C, and the points C, D and B.

Equivalently, two other names for the plane Q can be AEC and CDB.

EBD is not an acceptable name for plane Q because the points E, B and D are collinear points, that is they lie on the same line.

So, we have found that another name for $\overleftrightarrow{AB}$ can be $\overleftrightarrow{AC}$ , two other names for the plane Q can be AEC and CDB, and EBD is not an acceptable name for plane Q because the points E, B and D are collinear points.

Learn more about naming of lines and planes here:

answered: Guest

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answered: Guest

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