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3 Coordinate Geometry
CHAPTER
We are Starting from a Point but want to Make it a Circle of Infinite Radius
Cartesian Plane
Ordered pair – A pair of numbers a and b instead in a specific order with a at the first place and b at
the second place is called an ordered pair (a, b).
(a, b) (b, a)
Coordinate Geometry: The branch of mathematics in which geometric problems are solved through
algebra by using the coordinate system, is know as coordinate geometry.
Coordinate system: The position of a point in a plane is determined with reference to two fixed
mutually perpendicular lines, called the coordinate axes.
In the following figure: -
These lines are called the coordinate axes or the
axes of reference.
The horizontal line X’OX is called the X – axis.
The point O is called the origin.
Convention of signs: The distances measured
along OX, and OY are taken as positive and
those along OX’ and O’ Y’ are taken as negative.
Coordinates of a point in a plane.
Let P be a point in a plane.
Let the distance of P from the Y axis = a units and the distance of
p from the x axis = b units. Then we say that the
coordinates of P are (a, b)
a is called the x- coordinate.
The x – coordinate of a point is its perpendicular distance
from the Y axis measured along the x- axis and negative
along the negative direction of the x – axis). The x –
coordinate is also called the abscissa.
011-26925013/14 NTSE, NSO Coordinate Geometry
+91-9811134008 Diploma, XI Entrance
+91-9582231489 45
The Y- coordinate of a point is its perpendicular
distance from the x – axis measured along the y-
axis (Positive along eh positive direction of the y
–axis and negative along eh negative direction of
the y –axis). They y- coordinate is also called the
ordinate.
In the figure above.
b is called the y-coordinate or ordinate of P.
Quadrant: -
Let X’OX and YOY’ be the coordinate axes.
These axes divided by the plane of the paper into four region called Quadrants.
The XOY, YOX’, X’OY’ and Y’OX are respectively known as the first, second third, and fourth
quadrants.
Sings of the coordinates is various quadrants: -
Region Quadrant Nature of x and y Sign of Coordinate
XOY I X > O, Y > O ( +, +)
YOX’ II X < O, Y > O (–, + )
X’OY’ III X < O, Y < O (–, –)
Y’OX IV X > O, Y < O ( + , – )
Coordinates of a point on the x – axis: -
Every point on the x-axis is at a distance of 0 unit from the x axis. So, its ordinate is Thus, the
coordinates of every point on the y axis are of the form (x, 0).
Coordinates of a point on the y-axis: -
Every point on the y-axis is at a distance of unit from the y axis. So, pts abscissa is O.
Thus, the coordinates of every point on the y –axis are of the form (O, Y)
The coordinates of the origin are (O, O)
011-26925013/14 NTSE, NSO Coordinate Geometry
+91-9811134008 Diploma, XI Entrance 46
+91-9582231489
IX ACADEMIC QUESTIONS
Subjective
Assignment -1
1. Write down the coordinates of each points P,Q, R, S and T as show: -
2. Draw the lines X’OX and YOY’ as axes on a plane paper and Plot the points given below: -
(i) A (5, 3) (ii) B (– 3, 2 ) (iii) C (– 5, – 4) (iv) D (2, –6 )
3. In which quadrants do the given points lie:
(i) (4, – 2) (ii) (– 3, 7) (iii) (– 1, – 2) ( iv) (3, 6)
4. On which axes do the given points lie?
(i) (7, 0) (ii) (0, – 3) (iii) (0, 6) (iv) (–5, 0)
5. Draw the graph of the equation y = x3 + 2
6. Draw the graph of the equation y = 2x – 3
7. Draw the graph of the equation y = 2x.
8. Draw the lines XOX’ and YOY’ as the coordinate axes on a paper and plot the following points on it.
(i) P (7, 4) (ii) Q (– 5, 3) (iii) R (–6, –3) (iv) S (3, – 7)
(v) A (6, 0) (vi) B (0, 9) (vii) O (0, 0) (viii) C (– 3, 3)
9. On which axis do the following points lie?
(i) (7, 0) (ii) (0, – 5,) (iii) (0, 1) (iv) (– 4, 0)
10. In which quadrant do the given points lie
(i) (–6, 5) (ii) (–3, – 2) (iii) (2, –9) (iv) (2, 3 )
11. Draw the graph of the equation , y = x + 1
12. Draw the graph of the equation , y = 3x + 2
13. Draw the graph of the equation , y = 5x – 3
14. Draw the graph of the equation, y = 3x
011-26925013/14 NTSE, NSO Coordinate Geometry
+91-9811134008 Diploma, XI Entrance 47
+91-9582231489
15. Draw the graph of equation, y = – x
16. In which quadrant do the following will lie?
(i) (4,, 2) (ii) (–3, 5) (iii) (–2, –5) (iv) (4, –2 )
17. Plot the following points on a graph paper:
(i) (3, 4) (ii) (–2, 3 ) (iii) (–5, –2) (iv) (4, –3 )
18. Plot the following points on the graph paper: -
(i) P (3, 0) (ii) Q (– 4, 0) (iii) R (0, 5) (iv) S (0, – 7)
19. Write down the coordinates of the following point A, B, C, and D marked: -
20. Plot the following points on the graph paper: -
(i) (2,– 5) (ii) (4, – 3) (iii) (– 9, – 7) (iv) (7, – 4)
(v) (– 3, 2) (vi) (7, 0) (viii) (– 4, 0) (ix) (0, –4)
(x) (0, 0)
21. From the adjoining, find
(i) Abscissa
(ii) Ordinate
(iii) Coordinates of Point P. x
22. Write the answer of each of the following questions:
(i) What is the name of horizontal and the vertical lines drawn to determine the position and the
vertical lines Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
23. Determine
(i) Abscissa
011-26925013/14 NTSE, NSO Coordinate Geometry
+91-9811134008 Diploma, XI Entrance 48
+91-9582231489
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