Lines in Grade VII

Hello friends in this article we are going to discuss important geometrical topic that you study in grade VII. A line can be defined as a continuous extent of length, straight or curved, without breadth or thickness; The notion of the line was very first introduced by ancient mathematicians to represent straight objects and things with negligible width and depth. in more mathematical term the same can be defined as a geometrical object that is straight, infinitely long and infinitely thin. There are different types of lines like straight line, parallel line, perpendicular lines, intersecting lines, many more. Properties mean any qualities, features that are embedded in line.

Let’s focus on the properties of parallel lines. Parallel lines are those lines which move right next to each other and they move infinitely long but never cut each other. Properties of same said that, the two lines lie in the same plane, and do not intersect or cross each other. The properties of parallel line based on the Euclid’s parallel property means they can’t cut each other at any point. In other word the property says that lines are nothing with a pair of lines in a same plane which do not cut or meet each other. In this, we can introduce the other line called as transversal line that crosses a pair of parallel lines on a slant.

 

Let’s have an example of the properties of the parallel lines.    

Example 1:

Define the equation parallel to line 4q + 4p = 8 with the point (-6, 4).

Answer:

Given,

 4q + 4p = 8 and the point (-6, 4)

To detect the parallel line, we have to find the slope first.

For finding the slope, we need to change the given equation into slope intercept form.

4q + 4p = 8

Do addition of 4p on both sides of the equation,

4q + 4p = 8

- 4p = -4p

4q = -4p + 8

Divide by 4 on both sides,

q = (-p + 2)

The obtained equation is in the form, q= mp + b

So, the slope from the obtained equation m = -1

Generally, we know that the slope of parallel lines are equal i.e. m1 = m2

Here, m1 = -1

So, m2 = -1

The line equation is,

(q - q1) = m(p - p1)

(q - (4)) = -1 (p - (-6))

(q - (4)) = -(p + 6)

q - 4 = - x - 6

Subtract 4 on both sides,

q = -p - 2

Output: Thus, the pictures of parallel lines is given through the lines q= -p - 2, 4q + 4p = 8.

In this way we solve problems related to parallel lines. Geometry is very interesting mathematical part, that you can easily understand with help of bit practices. So do practice and score good marks and feel proud.