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Coordinate Geometry 
Important Points: 
1. To locate the position of an object or a point in a plane, we require two perpendicular 
lines. One of them is horizontal, and the other is vertical. 
2. The plane is called the Cartesian, or coordinate plane and the lines are called the 
coordinate axes. 
3. The horizontal line is called the x -axis, and the vertical line is called the y - axis. 
4. The coordinate axes divide the plane into four parts called quadrants. 
5. The point of intersection of the axes is called the origin. 
6. The distance of a point from the y - axis is called its x-coordinate, or abscissa, and 
the distance of the point from the x-axis is called its y-coordinate, or ordinate. 
7. If the abscissa of a point is x and the ordinate is y, then (x, y) are called the 
coordinates of the point. 
8. The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on 
the y-axis are (0, y). 
9. The coordinates of the origin are (0, 0). 
10. The coordinates of a point are of the form (+ , +) in the first quadrant, (–, +) in the 
second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant, where + 
denotes a positive real number and – denotes a negative real number. 
11. If x ? y, then (x, y) ? (y, x), and (x, y) = (y, x), if x = y. 
Page 2


Coordinate Geometry 
Important Points: 
1. To locate the position of an object or a point in a plane, we require two perpendicular 
lines. One of them is horizontal, and the other is vertical. 
2. The plane is called the Cartesian, or coordinate plane and the lines are called the 
coordinate axes. 
3. The horizontal line is called the x -axis, and the vertical line is called the y - axis. 
4. The coordinate axes divide the plane into four parts called quadrants. 
5. The point of intersection of the axes is called the origin. 
6. The distance of a point from the y - axis is called its x-coordinate, or abscissa, and 
the distance of the point from the x-axis is called its y-coordinate, or ordinate. 
7. If the abscissa of a point is x and the ordinate is y, then (x, y) are called the 
coordinates of the point. 
8. The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on 
the y-axis are (0, y). 
9. The coordinates of the origin are (0, 0). 
10. The coordinates of a point are of the form (+ , +) in the first quadrant, (–, +) in the 
second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant, where + 
denotes a positive real number and – denotes a negative real number. 
11. If x ? y, then (x, y) ? (y, x), and (x, y) = (y, x), if x = y. 
 
The best example of coordinates in everyday life is use of longitude and latitude on 
globe. Each unique location on the earth has a unique combination of longitude and 
latitude. Global positioning system used by radio taxi operators also uses x,y 
coordinates to find exact location of a vehicle. 
1.In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 
2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane. 
Finding exact location of a point from the origin 
This can be done by using formula, which looks complicated, and by using a graph 
paper. Suppose you need to calculate the following coordinates’ distance from origin: (-
2,4).  
Making a rough graphical representation will give you following figure: 
Page 3


Coordinate Geometry 
Important Points: 
1. To locate the position of an object or a point in a plane, we require two perpendicular 
lines. One of them is horizontal, and the other is vertical. 
2. The plane is called the Cartesian, or coordinate plane and the lines are called the 
coordinate axes. 
3. The horizontal line is called the x -axis, and the vertical line is called the y - axis. 
4. The coordinate axes divide the plane into four parts called quadrants. 
5. The point of intersection of the axes is called the origin. 
6. The distance of a point from the y - axis is called its x-coordinate, or abscissa, and 
the distance of the point from the x-axis is called its y-coordinate, or ordinate. 
7. If the abscissa of a point is x and the ordinate is y, then (x, y) are called the 
coordinates of the point. 
8. The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on 
the y-axis are (0, y). 
9. The coordinates of the origin are (0, 0). 
10. The coordinates of a point are of the form (+ , +) in the first quadrant, (–, +) in the 
second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant, where + 
denotes a positive real number and – denotes a negative real number. 
11. If x ? y, then (x, y) ? (y, x), and (x, y) = (y, x), if x = y. 
 
The best example of coordinates in everyday life is use of longitude and latitude on 
globe. Each unique location on the earth has a unique combination of longitude and 
latitude. Global positioning system used by radio taxi operators also uses x,y 
coordinates to find exact location of a vehicle. 
1.In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 
2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane. 
Finding exact location of a point from the origin 
This can be done by using formula, which looks complicated, and by using a graph 
paper. Suppose you need to calculate the following coordinates’ distance from origin: (-
2,4).  
Making a rough graphical representation will give you following figure: 
 
Here you get a point where perpendiculars from x and y axes are intersecting, all you 
need to calculate is the length of dotted arrow, which is the length of the point from 
origin. This dotted line is diagonal of the rectangle formed by perpendiculars from x and 
y axes. So the required answer will be: 
 
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FAQs on Coordinate Geometry Important Notes - Class 9

1. What is coordinate geometry?
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometric figures using coordinate systems. It involves representing points, lines, and shapes on a coordinate plane using the x and y coordinate axes.
2. How are coordinates represented in coordinate geometry?
Ans. In coordinate geometry, coordinates are represented by an ordered pair (x, y), where x represents the horizontal distance from the origin (x-axis) and y represents the vertical distance from the origin (y-axis). The x-coordinate is always written first, followed by the y-coordinate.
3. How can we find the distance between two points in coordinate geometry?
Ans. To find the distance between two points (x1, y1) and (x2, y2) in coordinate geometry, we can use the distance formula. The distance formula is √((x2 - x1)^2 + (y2 - y1)^2). By substituting the coordinates of the two points into this formula, we can calculate the distance between them.
4. What is the slope of a line in coordinate geometry?
Ans. The slope of a line in coordinate geometry represents the steepness or inclination of the line. It is a measure of how much the line rises or falls as we move horizontally along it. The slope is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
5. How do we determine the equation of a line in coordinate geometry?
Ans. To determine the equation of a line in coordinate geometry, we need to know either the slope of the line and a point on it or two points on the line. If we know the slope (m) and a point (x1, y1), we can use the point-slope form of the equation: y - y1 = m(x - x1). If we know two points (x1, y1) and (x2, y2), we can calculate the slope using the formula mentioned in the previous question and then use the slope-intercept form of the equation: y = mx + b, where b is the y-intercept.
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