Students in this video, let's discuss how to find the distance between two parallel lines.
All right.
Now, what is the characteristic of parallel lines?
They will have the same slope, right?
What do I mean with that?
So, for example, let me draw my axis over here and over here.
I have a line, right.
So this is a line.
Now, if you have a line that is parallel to this line, it will have the same slope.
So it looks something like this right over here.
You can see that these two lines will never intersect.
That's what we mean with parallel lines.
And you can see that they have the same slope right over here if I draw a line like this.
You can see it's forming an angle, detA, and you can notice that if I have another line like this,
this angle also will be equal to Peter.
Therefore, Tanty in both the cases will be the same and these two lines will have the same slope.
All right.
Now let's take the equation of two lines that are parallel.
So over here you have X plus by plus C, one is equal to zero.
And over here you have X plus by plus C, two is equal to zero.
Now, these two lines will be parallel to each other.
Why is that so?
Because both of them have the slope minus a baby.
Right.
And you know how to find this right.
You need to write this equation in the form Y is equal to IMEX policy.
So let's quickly do that over here.
This becomes B Y is equal to minus X minus one, or it becomes Y is equal to minus ebi B, X, minus
C1 by B and over here, minus Abib is the slope.
Right.
So that's what we have mentioned over here.
Now you can see that in both the lines, the slope is minus Abib and hence these two are parallel to
each other.
All right.
Now say you are given two parallel lines and you want to find the distance between these two lines.
All right.
Now, how do we do that?
We have an equation for that.
The distance between these two lines will be equal to C1 minus C two, divided by route of A squared,
plus B square.
And we are taking more over here because if you are getting the distance as a negative value, for example,
you substitute this part and you get the distance as negative three, then the answer would be positive
three.
So you always have to take the positive value because the distance can never be negative right now.
What would you have done if you did not know this equation?
You could have just found one point on any one line and you can find the distance of that point from
the other line also.
All right.
Now, we don't need to do that.
You know, the way over here to quickly find the distance between two parallel lines.