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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

Quadrants

XOY

X'OY

X'OY'

XOY'

(I)

(II)

(III)

(IV)

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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