Question

The diagram shows all the four quadrants in a Cartesian Plane.
Which of the following points below lies in \[3rd\] quadrant?
\[A( - 4,2)B(4,2)C(3, - 5)D( - 5, - 2)\]

Answer 1

Hint: We are given four different points out of which we have to identify which point lies in the third quadrant. If the two coordinates are in the form of \[(x,y)\], the points will lie in the third quadrant only if both coordinate values are negative i.e. \[( - x, - y)\].

Complete step by step solution:
The Cartesian plane creates four quadrants (I, II, III, IV).
We are given the diagram that shows all the four quadrants in a Cartesian Plane.
The points lies in \[3rd\] quadrant: \[A( - 4,2)B(4,2)C(3, - 5)D( - 5, - 2)\]

The coordinate point \[(x,y)\] on the Cartesian plane informs us about the horizontal distance of the point from the origin , and the vertical distance is \[y\]. If the sign of \[x\] is positive, the point is on the right of the origin; else it is on the left. Similarly, if the sign is positive for \[y\], the point is \[y\] points above the origin else it is \[y\] points below it.
Following points should be kept in mind about the points falling in the quadrants:
Quadrant I= Both the \[(x,y)\] coordinates are positive.
Quadrant II=Coordinate \[x\] is negative while coordinate \[y\] is positive.
Quadrant III= Both the \[(x,y)\] coordinates are negative.
Quadrant IV=Coordinate \[x\] is positive while coordinate \[y\] is negative.
It can be shown diagrammatically as follows:

It shows the positive and negative sign of coordinates falling in the four quadrants.
Now we can solve the question:
Out of all the points, only point \[D\] has both negative coordinates.
Hence, \[D( - 5, - 2)\] lies in the third quadrant.
The points given in the question can be plotted on the Cartesian plane as follows:

Note:
The Cartesian plane is defined as a two-dimensional coordinate plane, which is formed by the intersection of the \[X\]-axis and \[Y\]-axis.
The \[X\]-axis and \[Y\]-axis intersect perpendicular to each other at the point called the origin.