Question

Which of the following points lie in $III$ Quadrant?
A. $\left(1,3\right)$
B. $\left(-1,3\right)$
C. $\left(+1,-3\right)$
D. $\left(-1,-3\right)$

Answer 1

Hint: To find which point lies in the 3rd quadrant, we are going to see the theory of the Cartesian plane. In the first quadrant, both x and y coordinates are positive. In the second quadrant, x coordinate is negative and y coordinate is positive. In the third quadrant, both the coordinates are negative and in the fourth quadrant x coordinate is positive and y coordinate is negative. So, the point from the given four points which has both x and y coordinates negative will be lying in the 3rd quadrant.

Complete step by step solution:
In this question, we are given 4 coordinates and we need to determine out of these 4 which coordinate lies in the 3rd quadrant. First of all, let us see a little theory about the Cartesian plane.
In mathematics, the Cartesian plane is defined as a 2dimensional coordinate plane formed by the intersection of the x-axis and y-axis.
This x-axis and y-axis split the plane into four parts called quadrants. Let us see the figure of a Cartesian plane.

1st Quadrant:
First quadrant is formed by the X and Y axis, so the values of x and y coordinates are positive in the 1st quadrant.
 $\Rightarrow \left(x,y\right)=\left(+,+\right)$
2nd Quadrant:
Second quadrant is formed by the Y and X’ axis, so the value of y coordinate will be positive and the value of x coordinate will be negative in the 2nd quadrant.
 $\Rightarrow \left(x,y\right)=\left(-,+\right)$
3rd Quadrant:
Third quadrant is formed by the X’ an Y’ axis, so the values of both x and y coordinates will be negative in the 3rd quadrant.
 $\Rightarrow \left(x,y\right)=\left(-,-\right)$
4th Quadrant:
Fourth quadrant is formed by the X and Y’ axis, so the value of x coordinate will be positive and the value of y coordinate will be negative in 4th quadrant.
$\Rightarrow \left(x,y\right)=\left(+,-\right)$
Now, the given points are
 $\Rightarrow A\left(1,3\right)=\left(+,+\right)$
 $\Rightarrow B\left(-1,3\right)=\left(-,+\right)$
 $\Rightarrow C\left(+1,-3\right)=\left(+,-\right)$
 $\Rightarrow D\left(-1,-3\right)=\left(-,-\right)$

Therefore, we can see that point D has both the coordinates negative. Hence, $D\left(-3,-1\right)$ lies in the 3rd quadrant. Hence, option D is the correct answer.

Note: The ordered pair $\left(a,b\right)$ in the Cartesian plane is called the Cartesian coordinates. Here, the first number in the ordered pair is called abscissa. It is the distance of the point from the y axis. The second point in the ordered pair is called ordinate. It is the distance of the point from the x axis.