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Jun 4, 2024 · Points, Lines, and Planes are basic terms used in Geometry that have a specific meaning and are used to define the basis of geometry. We define a point as a location in 3-D or 2-D space that is represented using the coordinates. We define a line as a geometrical figure that is extended in both directions to infinity.
- 50 min
- Defining Lines. For the following exercises, use this line (Figure 10.4). Figure 10.4. Define DE¯DE¯. Define FF. Define DF↔DF↔. Define EF¯EF¯. Answer.
- Determining the Best Route. View the street map (Figure 10.7) as a series of line segments from point to point. For example, we have vertical line segments AB¯AB¯, BC¯,BC¯, and CD¯CD¯ on the right.
- Identifying Parallel and Perpendicular Lines. Identify the sets of parallel and perpendicular lines in Figure 10.10. Figure 10.10. Answer. Drawing these lines on a grid is the best way to distinguish which pairs of lines are parallel and which are perpendicular.
- Defining Union and Intersection of Sets. Use the line (Figure 10.12) for the following exercises. Draw each answer over the main drawing. Figure 10.12.
- Defining Lines. For the following exercises, use this line (Figure 10.4). Figure 10.4. Define DE¯DE¯. Define FF. Define DF↔DF↔. Define EF¯EF¯. Solution.
- Determining the Best Route. View the street map (Figure 10.6) as a series of line segments from point to point. For example, we have vertical line segments AB¯AB¯, BC¯,BC¯, and CD¯CD¯ on the right.
- Identifying Parallel and Perpendicular Lines. Identify the sets of parallel and perpendicular lines in Figure 10.9. Figure 10.9. Solution. Drawing these lines on a grid is the best way to distinguish which pairs of lines are parallel and which are perpendicular.
- Defining Union and Intersection of Sets. Use the line (Figure 10.10) for the following exercises. Draw each answer over the main drawing. Figure 10.10.
In geometry, points and lines are the fundamental concepts that we need to learn before we learn about different shapes and sizes. A point is a dimensionless shape, since it represents a dot only, whereas a line is a one-dimensional shape. Both points are lines used to draw different shapes and sizes in a plane.
- A point is a dot marked on a plane that represents the position.
- A line is a series of points that are connected by a straight path and extend infinitely in the opposite directions.
- The points on the same line are called collinear points.
- We need at least two points to determine the line.
- Lines do not have endpoints. They extend endlessly in the opposite direction.
- A point has zero size. It is dimensionless. It does not have length, width and height.
- Points. A “dot” on a piece of paper can be considered as a point. A point has no length, width, or height. It just specifies an exact location. It is zero-dimensional.
- Lines. A line is one-dimensional, that is, a line has length, but no width or height. A line extends forever in both directions. A line is uniquely determined by two points.
- Line Segment. A line segment connects two endpoints. A line segment with two endpoints, A and B, is denoted by. A line segment can also be drawn as part of a line.
- Mid-Point. The midpoint of a segment divides it into two segments of equal length. The diagram below shows the midpoint M of the line segment. Since M is the midpoint, we know that the lengths AM = MB.
A point is just a point and is labeled with a capital letter. An endlessly long, straight mark is known as a line and is labeled with two capital letters that represent two points on the line. A plane is a flat surface that never ends in any direction and is labeled with a capital letter along with the word "plane."
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Definition: Planes. A plane is a 2-dimensional surface made up of points that extends infinitely in all directions. There exists exactly one plane through any three noncollinear points. Of particular interest to us as we work with points, lines, and planes is how they interact with one another.
