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Coordinate Axes is considered one of the most asked concept.
15 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 :
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
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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