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High students, we have learned how to find a point that divides a given line segment in a given ratio

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right internally now in this video.

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Let's learn how to find a point that divides a given line segment in a given ratio externally.

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All right.

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Now, over here I have my x axis and y axis.

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Now let's identify two points, A and B, all right.

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Now, let's say you need to find point C, which divides a B externally in the ratio M is to one.

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Now, first, let's understand what this means and then we'll find out how to do this.

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All right.

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Now, over here we have point C, which lies on the line A, B, but which is external to line segment

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A, B, and the ratio of the lengths is C divided by B, C will be M is two and that is AC divided by

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B, C should be equal to MS two.

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And that is what we mean when we say that point.

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C divides AB in the ratio.

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M is two in externally.

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All right.

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Now let's proceed and find out how to do this.

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Let it be x1 y one and b b x2 y2.

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Now this point C over here will be m x2 minus N x1 by M minus one comma.

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And why do minus envie one by M minus in.

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All right.

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Now let me make some space over here.

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All right, now, let me tell you an easy matter to remember this, we already know how to find this

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if buoyancy was an internal division, right.

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So imagine buoyancy is internal and then this would be.

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And this is in.

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Right.

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KBE.

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And now in this case, what would have been the answer?

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It would have been X2.

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Plus in X1.

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Divided by M plus, and right now that's very easy to remember.

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We saw the pattern, right must be multiplied with the other one, which is farther away.

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And similarly, in with the one which is farther away, that's X one over here right now, because this

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is an external division.

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All you need to do is you need to change this plus into minus.

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This plus also becomes minus.

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And you get this equation over here.

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All right.

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Now, having known this, let's proceed.

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Let's try to find the external point of division of AB in the ratio.

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Two is to three.

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Right.

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And let it be to come A three and B, B, seven, comma six.

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Now, applying it to this equation over here, you will get the answer as to in the seven minus three

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in the two by two minus three comma two in the six minus three comma three by two minus three.

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Right.

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And this on solving gives you minus eight.

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Minus three.

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Now what does that mean?

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Let me expand the axis a bit.

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Alright.

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So we identify minus eight, minus three over here.

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Now you will find that this point over here also lies on this line and this point divides a B externally

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in the ratio two is two three.

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That means the distance, if this is see the distance A, C divided by B, C will be equal to two by

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three and you can see that visually also it is shorter compared to B C, right.

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That's because the numerator over here is lesser.