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Students in this video, let's discuss internal division of airline segment by a point.

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All right.

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So all year I have my X and Y axis and I identify two points over here.

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Let me join them and I call them A and B.

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All right.

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Now, say you have to find the point C, which divides a B in the ratio M is to end, but you need to

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find a point on a B that divides a B in the ratio M is to end.

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So what does that mean?

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For example, if this is the point C then the length of AC right.

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Divided by the length of C, B should be equal to erm is to an.

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All right, so that's what we are trying to find over here.

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Now let's take the coordinates of point ESX one white one and the ordinance of point B as to why two.

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All right.

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Now, then, the coordinates of point C such that it divides A B in the ratio M is to end will be M

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x2 plus next one by employers in comma and why two plus in y one by and plus in.

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Now over here you can notice the pattern over here is m right.

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You need to multiply it with whatever is on the other side and over here you have n that has to be multiplied

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with whatever is on the other side.

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So you have to multiply M with x2 and in with X1.

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You can see that over here M x2 plus an x1 and the denominator is emplacing and same is applicable in

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the case of the Y coordinate m y two plus in y one.

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And you need to divide that with emplacing.

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But this would be the point which divides a B in the ratio M is two in.

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All right, let's take an example over here and try to apply this formula so that we understand it better

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say this point is to come at three and let this point over here B 11, comma eight.

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And let's take aim is to end as two is two one.

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All right, now, if this is the case, then the point C would be to Endou 11 plus one in two by two

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plus one comma two in the eight plus one into three by two plus one.

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Over here you can see that M is to write in this one.

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So two has to be multiplied with eleven.

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That's two in the eleven over here and one has to be multiplied with one.

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So one in two by two plus one.

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Similarly two has to be multiplied with eight and one has to be multiplied with three.

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So two in the eight plus one in two three.

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That gives you the answer as eight Camonte 19 by three, the point eight comma 19 by three divides nine

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segment a B in the ratio two is two one.