Answer
Verified
375.9k+ views
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.
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.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE