Question

Find the quadrants in which the following points lie
[i] (3,2)
[ii] (-2,1)
[iii] (-1,-3)
[iv] (5,-1)

Answer 1

Hint: Plot these points on a graph paper and hence determine in which quadrant they lie.

Complete step-by-step answer:
Plotting point P(x,y) on a graph paper:
When plotting a point P(x,y), we move x units on x-axis and y units on the y-axis. If x is positive, then we move x units in the right direction. If x is negative, then we move on the x-axis in the left direction. If y is positive, then we move on the y-axis in the upwards direction. If y is negative, then we move on the y-axis in the downward direction. Finally, from these two positions we draw lines parallel to another axis, i.e. from a point on the x-axis we draw a line parallel to y-axis and from a point on y-axis, we draw a line parallel to the x-axis. The point at which these lines intersect gives the position of the point P(x,y) in the cartesian plane.
[i] Plotting (3,2):
We move 3 units on the x-axis in the rightward direction. From that position, we draw a line parallel to the y-axis.
We move 2 units on the y-axis in the upward direction. From that position, we draw a line parallel to the x-axis.
The lines intersect at point A.
The graph is shown below.

As is evident from the graph, A(3,2) lies in the first quadrant.

[ii] Plotting (-2,1):
We move 2 units on the x-axis in the leftward direction. From that position, we draw a line parallel to the y-axis.
We move 1 unit on the y-axis in the upward direction. From that position, we draw a line parallel to the x-axis.
The lines intersect at point A.
The graph is shown below.

As is evident from the graph A(-2,1) lies in the second quadrant.

[iii] Plotting (-1,-3):
We move 1 unit on the x-axis in the leftward direction. From that position, we draw a line parallel to the y-axis.
We move 3 units on the y-axis in the downward direction. From that position, we draw a line parallel to the x-axis.
The lines intersect at point A.
The graph is shown below.

As is evident from the graph A(-1,-3) lies in the third quadrant.

[iv] Plotting (5,-1):
We move 5 units on the x-axis in the rightward direction. From that position, we draw a line parallel to the y-axis.
We move 1 unit on the y-axis in the downward direction. From that position, we draw a line parallel to the x-axis.
The lines intersect at point A.
The graph is shown below.

As is evident from the graph A(5,-1) lies in the fourth quadrant.

Note: Alternatively, we can find the quadrant by remembering the following rules:
If x and y both are positive, then (x,y) lies in the first quadrant.
If x is negative and y is positive, then (x,y) lies in the second quadrant.
If x and y both are negative, then (x,y) lies in the third quadrant.
If x is positive and y is negative, then (x,y) lies in the fourth quadrant.
Hence we can find the respective quadrants of each of the points above.