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Chapter – 3
Coordinate Geometry
SOME BASIC CONCEPTS
Descartes invented the idea of placing two lines
perpendicular to each other on a plane, and locating
points on the plane by referring them to these lines. The
perpendicular lines may be in any direction. Combine
both the lines in such a way that the two lines cross each
other at their zeroes, or origins. The horizontal line XX’
is called the x - axis and the vertical line YY’ is called the
y - axis. The point where XX’ and YY’ cross is called the
origin, and is denoted by O. Since the positive numbers
lie on the directions OX and OY, OX and OY are called
the positive directions of the x - axis and the y - axis,
respectively.

The axes divide the plane into four parts. These four parts
are called the quadrants (one fourth part), numbered I, II,
III and IV anticlockwise from OX. So, the plane consists of the axes and
these quadrants. We call the plane, the Cartesian plane, or the
coordinate plane, or the xy-plane.
The axes are called the coordinate axes.

We write the coordinates of a point, using the following conventions:

(i) The x - coordinate of a point is its perpendicular distance from the y
– axis measured along the x -axis.
The x - coordinate is also called the abscissa.
For the point P, it is + 4 and for Q, it is – 6.
(ii) The y - coordinate of a point is its perpendicular distance from the x
– axis measured along the y - axis.
The y - coordinate is also called the ordinate.
For the point P, it is+ 3 and for Q, it is –2.
(iii) In stating the coordinates of a point in the coordinate plane,
the x – coordinate comes first, and then the y - coordinate. We
place the coordinates in brackets.
Hence, the coordinates of P are (4, 3) and the coordinates of Q
are (– 6, – 2).

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Exercise 3(a)
1. Write the answer of each of the following questions:
(i) What is the name of (a) horizontal line and the (b) vertical line drawn to determine the position of any
point in the Cartesian plane? (NCERT)
(ii) What is the point of intersection of the coordinate axes called? (NCERT)
(iii) What is the name of each part of the plane formed by these two lines (coordinate axes)? How many
such parts are there? (NCERT)
(iv) How is a point represented in a Cartesian system?
(v) What is the other name used for x-coordinate and y-coordinate of a point?
(vi) Define abscissa and ordinate of a point.
(vii) The coordinates of a point are (3, –4). What are abscissa and ordinate of the point?
(viii) In which quadrant(s), the abscissa of a point is positive?
(ix) In which quadrant(s), the ordinate of a point is negative?
(x) In which quadrant(s), the abscissa and ordinate of a point have different signs?
(xi) In which quadrant(s), the abscissa and ordinate of a point have same signs?

2. See Fig.1 and complete the following statements:

(NCERT)
(i) The abscissa and the ordinate of point B are ___
and ___, respectively. Hence, the coordinates of B
are (__, __).
(ii) The x-coordinate and the y-coordinate of the
point M are ___ and ___, respectively. Hence, the
coordinates of M are (__, __).
(iii) The x-coordinate and the y-coordinate of the
point L are _ _ _ and _ _ _, respectively. Hence, the
coordinates of L are (_ _, _ _).
(iv) The x-coordinate and the y-coordinate of the
point S are _ _ _ and _ _ _, respectively. Hence, the
coordinates of S are (_ _, _ _).

3. From the adjoining figures find

(i)(a) Abscissa (b) Ordinate (c) Coordinates of a point A
(ii) (a) Abscissa (b) Ordinate (c) Coordinates of a point B

4. Draw x-axis and y-axis and mark the points:

(i) A(4, 5), (ii) B(–4, 5), (iii) C(–4, –5),
(iv) D(4, –5), (v) E(2, 6),
(vi) F(3, –2), (vii) G(–1, 3), (viii) H(–2, –5)

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5. Without using graph, write the quadrants in which the following points lie
(i) A(3, –4) (ii) B(–3, 4) (iii) C(–3, –4)
(iv) D(3, 4) (v) E(–5, 6) (vi) F(–1, –2)
(vii) G(7, 9) (viii) H(2, –7)

6. Write the coordinates of the points marked on the axes in Fig.

(NCERT)

7. Plot the following points on a graph paper, by drawing x and y

axis:
(i) A(3, 0) (ii) B(0, 5)
(iii) C(–5, 0) (iv) D(0, –2)

8. See Fig.3, and write the following:

(i) The coordinates of B.
(ii) The coordinates of C.
(iii) The point identified by the
coordinates (–3, –5).
(iv) The point identified by the
coordinates (2, – 4).
(v) The abscissa of the point D.
(vi) The ordinate of the point H.
(vii) The coordinates of the point L.
(viii) The coordinates of the point M.

9. Answer the following questions:

(i) What are the coordinates of the point of intersection
of x and y axis? What is the point called?
(ii) What is the ordinate of a point on x-axis?
(iii) What is the abscissa of a point on y-axis?
(iv) If the y coordinate of a point is 0, the point lies on…..
(v) If the x coordinate of a point is 0, the point lies on ….
(vi) What will be the coordinates of a point on x-axis, which is on the right side of x-axis and at a distance
of 3 units from origin?
(vii) What will be the coordinates of a point on x-axis, which is on the left side of x-axis and at a distance of
3 units from origin?
(viii) What will be the coordinates of a point on y-axis, which is at a distance of 4 units above origin?
(ix) What will be the coordinates of a point on y-axis, which is at a distance of 2 units below origin?
(x) If a point lies on x-axis and has the coordinates (–5, a), what is the value of a?
(xi) If a point lies on y-axis and has the coordinates (b, 4), what could be the value of b?
(xii) What will be the perpendicular distance of the point (5, 4) from x-axis?
(xiii) What will be the perpendicular distance of the point (3, 7) from y-axis?
(xiv) What will be the distance of the point (0, –3) from origin?
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10. Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3) and (6, 1) in the Cartesian plane.
(NCERT)
11. Plot the following ordered pairs (x, y) of numbers as points in the Cartesian plane. Use the scale 1 cm = 1
unit on the axes. (NCERT)
x –3 0 –1 4 2 0
y 7 –3.5 –3 4 –3 –1.25

12. In which quadrant or on which axis do each of the points (– 2, 4), (3, –1), (–1, 0), (1, 2),(–3, –5) lie? Verify
your answer by locating them on the Cartesian plane. (NCERT)
13. Write the coordinates of the following points:
(i) A point whose perpendicular distance from the x and y axis are 6 and 3 respectively.
(ii) A point, lying in quadrant II and at a distance of 5 and 3 on x and y axis respectively.
14. Write the coordinates of a point:
a) Above x-axis and lying on y-axis at a distance of 5 units from the origin.
b) Below x-axis and lying on y-axis at a distance of 3 units from the origin.
c) Lying on x-axis to the right of origin at a distance of 4 units.
d) Lying on x-axis to the left of the origin at a distance of 3 units.
e) Lying on x and y axis both.

15. If (x + 2, 4) = (3, y – 1), find the values of x and y.

16. If the coordinates of a point can be written as (2p + 1, –5) or (5, 3q + 1), find values of p and q.
17. The perpendicular distance of a point from x axis is 2 units and the perpendicular distance from the y axis
is 3 units. Write the coordinates of the point, if it lies in the :
(a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant

Answers to questions of Exercise 3(a)

1.(i) (a) x-axis, (b) y-axis (ii) Origin (iii) Quadrants, 4 (iv) by its coord. (x, y)
(v) Abscissa, Ordinate (vii) Abscissa = 3, Ordinate = –4 (viii) I and IV (ix) III and IV
(x) II and IV (xi) I and III
2.(i)4; 3; (4, 3) (ii) –3;4; (–3,4) (iii)–5; – 4; (–5, –4) (iv) 3;–4;(3,–4)
3.(a) (i) 0, (ii) 0, (iii) (0, 0) (b) (i) 5, (ii) 2, (iii) (5, 2)
5.(i) IV, (ii) II, (iii) III, (iv) I, (v) II, (vi) III, (vii) I,
2
(viii) IV 6. A(4, 0); B(0, 3); C(–5, 0); D(0, –4); E(3 , 0) 8. (i) (–5, 2) (ii) (5, –5)
(iii) E (iv) G (v) 6 (vi) –3 (vii) (0,5) (viii) (–3, 0)
9.(i)Origin(0,0) (ii) zero (iii) zero (iv) x-axis (v) y-axis (vi) (3, 0) (vii) (–3, 0)
(viii) (0, 4) (ix) (0, –2) (x) a = 0 (xi) b = 0 (xii) 4 units (xiii) 3 units (xiv) 3 units
12. II; IV; x-axis; I; III 13. (i) (3, 6) (ii) (–5, 3)
14. (a) (0, 5) (b) (0, –3) (c) (4, 0) (d) (–3, 0) (e) (0, 0)
15. x = 1, y = 5 16. p = 2, q = –2 17. (a) (3, 2), (b) (–3, 2) (c) (–3, –2) (d) (3, –2)

Success is the progressive realization of a worthy goal.

Add: 5 Ga 19, Near St.Edmund’s school, Jawahar Nagar, Jaipur.
Ph: 0141-4036374 M: 9414063576