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.