Let's do this question, consider all zero zero eight to zero and be zero to be X, Y is a set of points
that satisfies X plus Y greater than two and X into Y greater than zero.
All right.
Now was the video.
Give it a try and then let's do it together.
All right, so we have to identify which among these false statements is correct about point B, right.
And B is a general point that speaks right now.
Let's plot the axis over here.
All right, now we know these three points that are given to us, let's applaud them.
And I have joined and be right to this point over here is zero zero, so this is all right, point A's
to zero.
So you have two units over here and zero units along the Y axis.
That's two zero.
And point B is zero to.
All right, now we need to find the point B, X, Y, such that X plus why is greater than two and X
into Y is greater than zero.
So as of now, we have not yet discussed the way to describe a line in the X Y plane.
But let's make a crude observation over here.
Now, any point that you take to this direction of this line will have X plus Y greater than two.
Is that true?
Let's try out let's take a point, say, over here.
Let this be four zero right now.
In this case, what is X plus?
Why, that's four plus zero, which gives you four.
And that is greater than two right now.
What about if I take a point over here, that's three three that also will have explores why greater
than two.
Right.
And if I take any point along this line, you will see that they will have values that X plus.
Why add up to two right now?
We will learn more about this when we learn how to describe or write the equation of a line in the X
Y plane.
But this is an introductory example.
So let's proceed with basic logic and crude observations.
All right.
Now, any point to this side of X plus why I just joined in.
We right.
Any point to this direction of this line will have X plus Y greater than two, right?
All right, so these sections will have X plus Y greater than two now over here, we need B, X, Y,
such that X plus why is greater than do so B has to be in this direction.
Right.
And it is mentioned that X into Y has to be greater than zero.
So if X and Y has to be greater than zero, either both of them should be positive or both of them should
be negative.
Right.
Let's take an example.
Two into three.
That gives you six.
That's greater than zero, right?
Two in the minus three.
That's minus six.
That is not greater than zero.
So that does not qualify.
What about minus two into three?
This is minus six.
So it does not qualify because it's not greater than zero.
What about minus two in the minus three.
That is six.
And that is greater than zero.
So these two qualify, right?
Therefore, either both of them should be positive or both of them should be negative.
All right.
We have discussed that the axis divide the X Y plane into four quadrants.
Right.
So these are the four quadrants now in these quadrants where all will X and Y be positive and where
will be X and Y negative?
Let's try to understand that C, I take a point in the first quadrant.
This could be two two.
Right.
This case, you can see that X is positive and Y is positive.
If I take a point over here, you can see that I have to move in the negative direction of the X axis.
Right.
So this over here could be minus two, two, two.
X is negative and Y is positive.
What about a point over here?
This one also requires moving in the negative direction in the X axis and in the negative direction
in the Y axis.
But this could be minus two, minus two.
And over here, if I take a point, say this could be two minus two, because it requires going in the
positive direction of the X axis and in the negative direction of the Y axis.
So it's positive two and then negative two.
Now you can see that X and Y are positive in the first quadrant and X and Y are negative in the third
quadrant to ask for this criteria.
Point B can either be in the first or the third quadrant.
All right.
Now, as per this criteria, that X plus why it has to be greater than two, right?
It cannot be in the third quadrant.
You can see that you have some points in the first quadrant, second quadrant and fourth quadrant,
which satisfies X plus.
Why greater than two?
But there is no point over here.
Therefore, taking these two conditions together, taking these two conditions together, that is first
quadrant is this section and X plus.
Why greater than two is anything to this side of this line, these two conditions together we get that.
The answer is option B, that is B lies outside triangle or A, B and is in the first quadrant.
And that is your answer to this question.