Question

Point ( 3,5 ) lies in which quadrant in the Cartesian coordinate plane?
(a) first quadrant
(b) second quadrant
(c) third quadrant
(d) fourth quadrant

Answer 1

Hint: We will look at the x-axis and the y-axis, and the plane formed by these two axes. We will study the four quadrants formed by these axes by seeing the change in the x-coordinate and the y-coordinate in every quadrant. Then we will compare the signs of the coordinates of the given point to the coordinates in different quadrants to find the quadrant in which the given point lies.

Complete step by step answer:
The Cartesian coordinate plane formed by the x-axis and the y-axis looks like the following figure,

In the figure above, we can see that the Cartesian coordinate plane is divided into four quadrants. The first quadrant consists of all points that have positive x-coordinates and positive y-coordinates. The second quadrant has points with negative x-coordinates and positive y-coordinates. In the third quadrant, all the points have negative x-coordinates and negative y-coordinates. The fourth quadrant has points with positive x-coordinates and negative y-coordinates.
The given point is $\left( 3,5 \right)$. The x-coordinate is positive. So, the point will lie in the first or the fourth quadrant. The y-coordinate of the given point is also positive. This implies that the point cannot be in the fourth quadrant. The given point lies in the first quadrant.
Hence, the correct option is (a).

Note:
We should be familiar with the workings of the Cartesian coordinate plane. We use this plane to plot points, graphs of functions, etc. The quadrants of this plane help us understand the properties of the points or the functions plotted on the plane. The x-coordinate of a point on this plane tells us the distance of the point from the x-axis. Similarly, the y-coordinate of a point on this plane tells us the distance of the point from the y-axis.