Points, Lines And Planes

Points, Lines and Planes are the undefined terms that provide the starting place for geometry or plane geometry. One of the easiest section in CAT quantitative aptitude is points, lines and planes. These topics are grouped together since they deal with the portion of Quantitative Aptitude that can be visualized. The definition and various properties of points, lines and planes are discussed below.

Points

A point is thought as a “dot” on a piece of paper. A point has no length, width, or height. It just specifies an exact location. It is zero-dimensional. The following is a diagram of points A, B, and M.

Points

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.

Lines

The line passing through the points A and B is denoted by

Line Segment

A line segment connects two endpoints. A line segment with two endpoints A and B is denoted by .

Line segments

A line segment can also be drawn as part of a line.

Line segments

Mid-Point

The midpoint of a segment divides the segment 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.

Midpoint

Rays

A ray starts from one endpoint and extends forever in one direction.

Rays

A ray starting from point A and passing through B is denoted by. Planes are two-dimensional. A plane has length and width, but no height, and extends infinitely on all sides. Planes are thought of as flat surfaces, like a tabletop. A plane is made up of an infinite amount of lines. Two-dimensional figures are called plane figures.

Rays

Space

Space is the set of all points in the three dimensions – length, width, and height. It is made up of an infinite number of planes. Figures in space are called solids.

Space

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