Students in this video, let's discuss internal division of airline segment by a point.
All right.
So all year I have my X and Y axis and I identify two points over here.
Let me join them and I call them A and B.
All right.
Now, say you have to find the point C, which divides a B in the ratio M is to end, but you need to
find a point on a B that divides a B in the ratio M is to end.
So what does that mean?
For example, if this is the point C then the length of AC right.
Divided by the length of C, B should be equal to erm is to an.
All right, so that's what we are trying to find over here.
Now let's take the coordinates of point ESX one white one and the ordinance of point B as to why two.
All right.
Now, then, the coordinates of point C such that it divides A B in the ratio M is to end will be M
x2 plus next one by employers in comma and why two plus in y one by and plus in.
Now over here you can notice the pattern over here is m right.
You need to multiply it with whatever is on the other side and over here you have n that has to be multiplied
with whatever is on the other side.
So you have to multiply M with x2 and in with X1.
You can see that over here M x2 plus an x1 and the denominator is emplacing and same is applicable in
the case of the Y coordinate m y two plus in y one.
And you need to divide that with emplacing.
But this would be the point which divides a B in the ratio M is two in.
All right, let's take an example over here and try to apply this formula so that we understand it better
say this point is to come at three and let this point over here B 11, comma eight.
And let's take aim is to end as two is two one.
All right, now, if this is the case, then the point C would be to Endou 11 plus one in two by two
plus one comma two in the eight plus one into three by two plus one.
Over here you can see that M is to write in this one.
So two has to be multiplied with eleven.
That's two in the eleven over here and one has to be multiplied with one.
So one in two by two plus one.
Similarly two has to be multiplied with eight and one has to be multiplied with three.
So two in the eight plus one in two three.
That gives you the answer as eight Camonte 19 by three, the point eight comma 19 by three divides nine
segment a B in the ratio two is two one.