Coordinate Axes - Practice Questions & MCQ

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 the figure below. 

A two-dimensional plane where the

The X-axis is the horizontal axis.

The 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

Polar Coordinate of a Point

Consider the figure,

If $O P=r$ and $\angle X O P=\Theta$. Then, the ordered pair of real numbers $(r, \Theta)$ called the polar coordinates of the point $P$.

From the figure

$
\begin{aligned}
& O M=x=r \cos \theta \\
& P M=y=r \sin \Theta
\end{aligned}
$
Square and add,

$
\begin{aligned}
& \mathrm{OM}^2+\mathrm{PM}^2=\mathrm{x}^2+\mathrm{y}^2=\mathrm{r}^2 \\
& \Rightarrow \mathrm{r}=\sqrt{\mathrm{x}^2+\mathrm{y}^2}
\end{aligned}
$

Example 1: Point $(-5,2)$ lies in which quadrant.
Solution: From the table, X -the coordinate is -ve and Y -coordinate is + ve. So, the point lies on the 2nd quadrant.
Example 2: A point lies on the X-axis at a distance of 10 units from the Y-axis, then coordinates of the point will be So, the coordinate of the point will be $(-10,0)$ or $(+10,0)$