High students, we have learned how to find a point that divides a given line segment in a given ratio
right internally now in this video.
Let's learn how to find a point that divides a given line segment in a given ratio externally.
All right.
Now, over here I have my x axis and y axis.
Now let's identify two points, A and B, all right.
Now, let's say you need to find point C, which divides a B externally in the ratio M is to one.
Now, first, let's understand what this means and then we'll find out how to do this.
All right.
Now, over here we have point C, which lies on the line A, B, but which is external to line segment
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
B, C should be equal to MS two.
And that is what we mean when we say that point.
C divides AB in the ratio.
M is two in externally.
All right.
Now let's proceed and find out how to do this.
Let it be x1 y one and b b x2 y2.
Now this point C over here will be m x2 minus N x1 by M minus one comma.
And why do minus envie one by M minus in.
All right.
Now let me make some space over here.
All right, now, let me tell you an easy matter to remember this, we already know how to find this
if buoyancy was an internal division, right.
So imagine buoyancy is internal and then this would be.
And this is in.
Right.
KBE.
And now in this case, what would have been the answer?
It would have been X2.
Plus in X1.
Divided by M plus, and right now that's very easy to remember.
We saw the pattern, right must be multiplied with the other one, which is farther away.
And similarly, in with the one which is farther away, that's X one over here right now, because this
is an external division.
All you need to do is you need to change this plus into minus.
This plus also becomes minus.
And you get this equation over here.
All right.
Now, having known this, let's proceed.
Let's try to find the external point of division of AB in the ratio.
Two is to three.
Right.
And let it be to come A three and B, B, seven, comma six.
Now, applying it to this equation over here, you will get the answer as to in the seven minus three
in the two by two minus three comma two in the six minus three comma three by two minus three.
Right.
And this on solving gives you minus eight.
Minus three.
Now what does that mean?
Let me expand the axis a bit.
Alright.
So we identify minus eight, minus three over here.
Now you will find that this point over here also lies on this line and this point divides a B externally
in the ratio two is two three.
That means the distance, if this is see the distance A, C divided by B, C will be equal to two by
three and you can see that visually also it is shorter compared to B C, right.
That's because the numerator over here is lesser.