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Coordinate Axes - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Coordinate Axes is considered one of the most asked concept.

  • 15 Questions around this concept.

Solve by difficulty

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is :

Concepts Covered - 1

Coordinate Axes

Coordinate Axes

The Cartesian coordinate system, also called a rectangular coordinate system, is based on a two-dimensional plane consisting of the x-axis and the y-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant; the quadrants are numbered counterclockwise as shown in figure below 

A two-dimensional plane where the

  • x-axis is the horizontal axis

  • y-axis is the vertical axis

A point in the plane is defined as an ordered pair, (x,y), such that x is determined by its horizontal distance from the origin and y is determined by its vertical distance from the origin.

The distance from a point to the vertical or y-axis is called the abscissa or x-coordinate of the point.

The distance from a point to the horizontal or x-axis is called the ordinate or y-coordinate of the point.

We can represent the point  (3,−1) in the plane by moving three units to the right  of the origin in the horizontal direction, and one unit down in the vertical direction.

Conversion Sign of coordinate










X- coordinate sign





Y-coordinate sign





Sign of (x, y)

(+, +)

(-, +)

(-, -)

(+, -)


Polar Coordinate of a Point

Consider the figure,

If OP = r and ∠XOP = Θ. Then, the ordered pair of real numbers (r, Θ) called the polar coordinates of the point P.

From the figure

OM = x = r cos Θ

PM = y = r sin Θ

\\\text{Square and add,}\\\\\mathrm{OM^2+PM^2=x^2+y^2=r^2}\\\\\mathrm{\Rightarrow r=\sqrt{x^2+y^2}}


Example 1 : Point (-5, 2) lies in which quadrant.

Solution:From the table, X-coordinate is -ve and Y-coordinate is +ve. So, the point lies on 2nd quadrant.  


Example 2: A point lies on X-axis at a distance of 10 units from Y-axis, then the coordinates of the point will be 

Solution : Given that point lies on X-axis at a distance of 10 units from the Y-axis, so the point may be on the left of the Y-axis or right of the Y-axis. So, X-coordinate will be -10 or +10. And, point lies on X-axis, so Y-coordinate will be 0.

So, the coordinate of the point will be (-10, 0) or (+10, 0)     

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Coordinate Axes

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