Question

In which quadrant or on which axis do each of the points\[\left( { - 2,{\text{ }}4} \right),{\text{ }}\left( {3,{\text{ }} - 1} \right),{\text{ }}\left( { - 1,0} \right),\left( {1,2} \right){\text{ and }}\left( { - 3, - 5} \right)\] lie?
Verify your answer by locating them on the Cartesian plane.

Answer 1

Hint:Notice the sign of the coordinates in each point and compare them with the standard form of the quadrants to find the answer.

Complete step-by-step answer:
We have given some points\[\left( { - 2,{\text{ }}4} \right),{\text{ }}\left( {3,{\text{ }} - 1} \right),{\text{ }}\left( { - 1,0} \right),\left( {1,2} \right){\text{ and }}\left( { - 3, - 5} \right)\].
The goal of the problem is to find the location of these points on the Cartesian plane.
We know about the quadrant that:
 1st quadrant → $\left( {x,y} \right)$[Both $x$ and $y$ are positive]
2nd quadrant → $\left( { - x,y} \right)$ [$x$ is negative, $y$ is positive]
3rd quadrant → $\left( { - x, - y} \right)$ [Both $x$ and$y$ are negative]
4th quadrant → $\left( {x, - y} \right)$ [$x$ is positive, $y$ is negative]
Let us take each point one by one and compare it with these standard forms of the quadrants.
$\left( { - 2,4} \right)$, it can be seen that the $x - $ coordinate of the point is negative and the $y - $ coordinate of the given point is positive, thus this point lies in the second quadrant.
$\left( {3, - 1} \right)$, it can be seen that the $x - $ coordinate of the point is positive and the $y - $ coordinate of the given point is negative, thus this point lies in the fourth quadrant.
$\left( { - 1,0} \right)$, it can be seen that the $x - $ coordinate of the point is negative but the coordinate of the given point is zero it shows that the given point is on the $x - $axis.
$\left( {1,2} \right)$, it can be noticed that both $x$ and $y - $coordinates of the point are positive; it means that this point lies in the first quadrant.
$\left( { - 3, - 5} \right)$, here both $x$ and $y - $coordinates of the point are negative, therefore these points lie on the third co-ordinate.
Let us verify our answer by looking at the graph below that has all the points plotted on it.

Note:When the $y - $coordinate of the point is $0$, then the point always lies on the $x - $axis, and when the $x - $coordinate of the point is $0$ then the point always lies on the $y - $axis.