Let's do this question three, your points, a common currency are such that Abe is equal to three B.C.,
the coordinates of A and B are three comma six and eight comma, minus two, respectively.
Now we need to find the coordinates of.
All right.
Pause the video, give it a try and then let's do it together.
All right.
We're back.
I hope you have given it a try.
Let's do it together.
Let me draw the axis and the points.
So this is point eight.
That's three comma six.
Right.
And this is point B, that's eight comma minus two.
Now, let me join them.
Now we need to find point C, right.
Such that AB is equal to three B.C. Now C can be in two places.
Right.
It could be somewhere over here or it can be somewhere over here right now.
If the point C is over here, then it means that this to this would be two is two one.
Right this length ac to B would be two is to one.
Right.
Why is that.
So that's because it's given that AB is equal to three B C right now.
If Boise's over here, let me take CBS length X and then AB is equal to three X.
Right.
And from the diagram you can see that if AB is three X and Qutb's X, then AC it would be two X.
That's why if C's over here then it means that C divide line segment AB in the ratio two is to one.
All right, now we know how to find the coordinates of point C in this case.
Right.
That would be two in two, eight plus three divided by two plus one comma two in the minus two plus
six by two plus one.
Right.
And that gives you on simplification.
Nineteen by three comma two by three.
Now you can see that this is not one of the options.
Right.
So that is not the answer.
And remember in the question, it says that the coordinates of C can be.
Now, if this was there in the option, it would have been the answer because this can be the coordinates,
but we don't have this in the options.
Therefore, this will be the answer.
And we need to find this one over here.
All right.
Now let's proceed.
Now we find this point over here.
All right, now you can see that you actually do not need to solve and find this point.
I will show you how to find it.
But can you tell me why you don't need to solve the at this point and you can directly mark the answers
option B, because visually you can see that this point over here will light in the fourth quadrant.
Right.
And there is only one solution, even among A, B and C and which is in the fourth quadrant, in the
fourth quadrant, X is positive.
Right.
X is positive and Y is negative.
And there is only one solution right over here.
X is positive and why is positive.
So it's not in the fourth quadrant in option C, both are negative.
That's the third quadrant in option D, X is negative and Y is positive.
That's the second quadrant.
So only option B's in the fourth quarter and therefore directly without solving, you can mark the answer
as option B..
Now let's proceed and see how you get this answer over here.
Now, if Point C is over here, then can we say that A C divided by B, C is equal to four by one.
Yes, we can say that, right?
Why is that so it's given that a B is equal to three B C right over here.
If A, B is three, ABC and BKS, X to A, B would be three X and A, C would be three X plus X.
That's for X, right.
AC.
And c.B would be X, therefore CE device externally, the line segment B in the ratio or is to one,
and then knowing this, we know how to find C, right?
We just apply the formula.
So the answer of C would be 14 to eight, minus six by four minus one comma or minus two, minus six
by four minus one.
And that simplifies to twenty six by three comma minus fourteen by three.
And that is option B..
Over here.