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

Solution: In first quadrant, value of $x$ coordinate is positive and value of $y$ coordinate is positive.
In second quadrant, value of $x$ coordinate is negative and value of $y$ coordinate is positive.
In third quadrant, value of $x$ coordinate is negative and value of $y$ coordinate is negative.
In fourth quadrant, value of $x$ coordinate is positive and value of $y$ coordinate is negative.

On the basis of above,
Point(-2,4) lies in second quadrant.
Point(3,-1) lies in fourth quadrant.
Point(-1,0) lies on x-axis as y coordinate is $0$
Point(1,2) lies in first quadrant.
Point(-3,-5) lies in third quadrant.