 # Points, Lines and Shapes – Definition, Types, Properties, Examples

In Mathematics, geometry deals with drawing various shapes and figures. we will discuss the properties of a point, definitions of a point, line, and shape, Types of points, different types of lines with solved examples. From Point, we can draw lines and shapes based on our requirements.

## Point – Definition

Point is defined as the exact location in the space. For a graphical representation, a Point is represented by ‘.’.A point can be represented as the intersection of two lines. #### Properties of a Point

• A point does not have any length, width, height, shape, size.
• It is the starting point to draw any figure or shape.
• A marked point is labeled by the capital letters.
• It has no dimension
• A point can be actual or implied.

### Types of Points

Here we will discuss the types of points. They are 1. Collinear points 2. Noncollinear points 3. Coplanar points 4. Noncoplanar points.

#### Collinear Points

If the group of points lies on the same line then they are called collinear points. Here all points lie on the same line. For example in the below figure A B and C are collinear points. #### Noncollinear Points

If the group of points does not lie on the same line then they are called non-collinear points. In the above figure, D E, F is non-collinear points.

#### Coplanar Points

If a group of points lies on the same plane then they are said to be coplanar points. In the below figure A, B, C is coplanar points. #### Non-Coplanar Points

A group of points that do not exist on the same plane is called non-coplanar points. In the above figure D, E is noncoplanar points.

### Line – Definition

A series of points extended by a straight path is defined as a line.

#### Properties of a Line

• A line is specifically denoted by two points marked in capital letters
• It extends indefinitely in both the directions
• The length of a line is undefined
• It is denoted by the following notation $$\overline{AB}$$.

### Types of Lines

Here we will discuss the types of lines.

#### Horizontal Lines

A straight line that is mapped from left to right is called a Horizontal line. #### Vertical Lines

A  straight line from bottom to top is called a Vertical line. It is the opposite of horizontal. #### Parallel Lines

Two lines are said to be parallel if they do not meet each other and intersect at any point. In the below figure two lines are said to be parallel lines. #### Perpendicular Lines

If two lines meet or intersect exactly at 90 0 then the lines are said to be perpendicular lines. #### Intersect Lines

If two lines meet at a point then the lines are said to be intersecting lines. ### Shape

The shape is defined as the outline of the object. Shapes can be divided into two types. 1. open shape 2. close shape.

#### Open Shape

It is a figure with line segments. At least one line segment does not meet the other. It is called open shape. ### Close Shape

It is a figure whose line segments are connected. It is the enclosed form. Closed shapes can be divided into two types. 1. Two-Dimensional shapes 2. Three Dimensional Shapes. Examples of two-Dimensional are square, rectangle, parallelogram, etc. Examples of three-Dimensional are Cube, Cylinder, sphere, etc. ### Points, Lines, and Shapes Examples

Example 1:

Find the coplanar points and noncoplanar points in the diagram below? Solution:

Points A, B, D, E are on the same plane. So they are Coplanar Points.

Points C, F is not on the same plane. So they are Noncoplanar.

Example 2:

Which are Collinear points and which are noncollinear points? Solution:

Points A, D exists on the same line. So they are Collinear points.

Points C, F, B, E do not exist in the same line. So they are Noncollinear points.

Example 3:

Find the point of intersection of both the lines l1 and l2? Solution:

The lines l1 and l2 intersect at point O. So the point of intersection is O.

### FAQs On Points, Lines, and Shapes

1. What are Coplanar points?

If the group of points exists in the same plane. It is called Coplanar points.

2. What are Collinear points?

If the set of points exists on the same line. It is called Collinear points.

3. What are Perpendicular lines?

If two lines meet or intersect exactly at 90 degrees then the two lines are said to be perpendicular lines.

4. What are intersecting lines?

If two lines meet at any point then the lines are called intersecting lines.

5. What are parallel lines?

If two lines do not meet and intersect at any point then the two lines are said to be parallel lines.

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