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Coordinate Axes is considered one of the most asked concept.
21 Questions around this concept.
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 :
If $ 'A' = (2,3) , 'B' = (3,-5) , 'C' = (-7,2 ) , 'D' (-1,-4) $ then choose the correct option
If $A = (3,5)$ and $B = (2,7)$ then ( abscissa A - abscissa B ) = ?
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If $A = (3,5)$ and $B = (2,7)$ then ( ordinate A - ordinate B) = ??
Name 2 axes used for references for measuring coordination in the cartesian system of rectangular coordinates.
What is the equation of line parallel to $\mathrm{y}=2$ and passing through a point in the x-axis where abscissa $=5$?
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
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 $O P=r$ 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 $(+10,0)$
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