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Students in this video, let's discuss how to find the distance between two parallel lines.

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All right.

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Now, what is the characteristic of parallel lines?

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They will have the same slope, right?

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What do I mean with that?

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So, for example, let me draw my axis over here and over here.

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I have a line, right.

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So this is a line.

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Now, if you have a line that is parallel to this line, it will have the same slope.

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So it looks something like this right over here.

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You can see that these two lines will never intersect.

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That's what we mean with parallel lines.

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And you can see that they have the same slope right over here if I draw a line like this.

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You can see it's forming an angle, detA, and you can notice that if I have another line like this,

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this angle also will be equal to Peter.

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Therefore, Tanty in both the cases will be the same and these two lines will have the same slope.

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All right.

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Now let's take the equation of two lines that are parallel.

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So over here you have X plus by plus C, one is equal to zero.

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And over here you have X plus by plus C, two is equal to zero.

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Now, these two lines will be parallel to each other.

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Why is that so?

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Because both of them have the slope minus a baby.

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Right.

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And you know how to find this right.

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You need to write this equation in the form Y is equal to IMEX policy.

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So let's quickly do that over here.

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This becomes B Y is equal to minus X minus one, or it becomes Y is equal to minus ebi B, X, minus

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C1 by B and over here, minus Abib is the slope.

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Right.

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So that's what we have mentioned over here.

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Now you can see that in both the lines, the slope is minus Abib and hence these two are parallel to

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each other.

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All right.

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Now say you are given two parallel lines and you want to find the distance between these two lines.

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All right.

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Now, how do we do that?

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We have an equation for that.

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The distance between these two lines will be equal to C1 minus C two, divided by route of A squared,

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plus B square.

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And we are taking more over here because if you are getting the distance as a negative value, for example,

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you substitute this part and you get the distance as negative three, then the answer would be positive

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three.

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So you always have to take the positive value because the distance can never be negative right now.

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What would you have done if you did not know this equation?

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You could have just found one point on any one line and you can find the distance of that point from

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the other line also.

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All right.

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Now, we don't need to do that.

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You know, the way over here to quickly find the distance between two parallel lines.