Assignment - Coordinate Geometry, Class 9 Mathematics PDF Download

FILL IN THE BLANKS

See figure and complete the following

1. The abscissa and the ordinate of the point B are _____ and _____respectively. Hence the coordinate of B are (____,____)

2. The x-coordinate and y-coordinate of the point M are _____ and _____respectively. Hence the coordinate of M are (____,____)

3. The x-coordinate and y-coordinate of the point L are _____ and _____respectively. Hence the coordinate of L are (____,____)

4. The x-coordinate and y-coordinate of the point S are _____ and _____respectively. Hence the coordinate of S are (____,____)

MATCH THE FOLLOWING

1. x > 0, y > 0       [ ]       [A] Q2

2. x < 0, y > 0       [ ]       [B] Q1

3. x < 0, y < 0       [ ]       [C] –ve X-axis

4. x > 0, y < 0       [ ]       [D] Q3

5. x > 0, y = 0       [ ]       [E] +ve X-axis

6. x < 0, y = 0       [ ]       [F] +ve Y-axis

7. x = 0, y < 0       [ ]       [G] Q4

8. x = 0, y > 0       [ ]       [H] –ve Y–axis

VERY SHORT ANSWER TYPE QUESTION

1. See figure and write the following

(i) The coordinates of B.
(ii) The coordinates of C.
(iii) The point indentified 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.

2. 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 of any point in the 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.

3. In the adjoining figure and

(i) Abscissa X' X
(ii) Ordinate
(iii) Co-ordinate of point P

4. Determine

(i) Abscissa
(ii) Ordinate
(iii) Co-ordinate of point P in this given figure.

5. Determine

(i) Abscissa
(ii) Ordinate
(iii) Co-ordinate of point P, in the figure.

6. In the given figure find :

(i) Abscissa X' X
(ii) Ordinate
(iii) Co-ordinate of point P, in the figure.

7. Write down :

(i) Abscissa
(ii) Ordinate
(iii) Co-ordinate of point P, Q, R and S.

8. Draw a rectangle KLMN such that its vertices K, L, M and N are (5, 0), (5, 3), (0, 3) and (0, 0) respectively.

9. Draw a rectangle ABCD such that its vertices A, B, C and D are (4, 3), (4, –2), (–7, –2) and (–7, 3) respectively.

10. Draw a rhombus ABCD whose vertices are (1, 4.5), (–1, 0), (1, –4.5) and (3, 0) respectively.

11. Draw a triangle ABC whose vertices A, B and C are (–3, 0), (3, 3) and (–3, 3) respectively.

12. Draw a square PQRS whose vertices P, Q, R and S are (0, 0), (–4, 0), (–4, –4) and (0, –4) respectively.

13. Construct a trapezium ABCD whose vertices A, B, C and D are (3, 0), (7, 9), (–6, 9) and (–2, 0) respectively.

14. Draw a parallelogram ABCD whose vertices A, B, C and D are (–4, 8), (–4, 2), (6, –7) and (6, –1) respectively.

15. Name the quadrants in which the following points lie:

(i) P(4,4)
(ii) Q(– 4,4)
(iii) R(– 4,– 4)
(iv) S(4,– 4).

16. Write coordinates of a point P if its distance from x-axis is 6 units and that of from y-axis is 1 unit.

17. In which quadrant or on which axis does the point (0, –3) lie ?

VERY SHORT ANSWER TYPE QUESTIONS

18. Plot the points (0, 0), (2, 3), (–2,3), (–4, –3) and (5, –1) in a rectangular co-ordinate system.

19. In which quadrant will the point lie, if:

(i) The y-coordinate is –3 and the x-coordinate is 4 ?
(ii) The x-coordinate is –5 and the y-coordinate is – 3 ?
(iii) The y-coordinate is 4 and the x-coordinate is 5 ?
(iv)The y-coordinate is 4 and the x-coordinate is –4 ?

20. Draw the quadrilateral whose vertices are:

(i) (1, I), (2,4), (8, 4) and (10,1)
(ii) (– 2, – 2), (– 4,2), (–6, –2) and (–4, –6).

21. Plot the following points in rectangular coordinate system. In which quadrant do they lie?
(i) (4,5)
(ii) (4, –5)
(iii) (–10,2)
(iv) (–10, –2)
(v) (– 7,5)
(vi) (9, –3).

22. Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3) and (6, 1) in the cartesian plane.

23. Plot the following pairs of number as points in the cartesian plane. Use the scale 1 cm = 1 unit on the axes.

24. Plot the point (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

25. On the graph paper sketch the parallelogram whose vertices are P(0, –3), Q(5, –3), R(8, 1) and S(3, 1). Also find its area.

26. Plot the vertices A(2, –3), B(4, 3), C(–3, 6) of ΔABC.
27. Plot the points in the plane if their coordinates are given as A(5, 0), B(0, 3), C(7, 2), D(–4, 3), E(–3, –2) and F(3, –2).

28. Plot the points A, B, C, D, E on the coordinate axes and name the figure formed by joining the points in order.

29. If a point lies on x and y axes both then write the name and coordinate of that point.

30. If abscissa and ordinate of a point are –ve and +ve respectively then in which quadrant this point lies.

31. Through how many maximum number of quadrant can a straight line pass.

Find the the distance between the points (Q.32 to Q.35)
32. (–4, 3), (0, 0)

33. (–4, 7), (3, –2)

34. (3, 3), (–1, –1)

35. (2, 4), (–6, 4)

36. Find the point on the x-axis which is equidistance from (–2, 5) and (2, –3).

37. Find the point on the y-axis which is equidistance from the point (5, 4) and (–2, 3).

38. Find the length of the sides of the triangle whose vertices are (–3, 4), (4, 0) and (0, –5).

39. Show that :

(i) (4, 4), (3, 5), (–1, 1) are the vertices of a right triangle.
(ii) (4, 3), (7, –1), (9, 3) are the vertices of an isosceles triangle.
(iii) (1, 1), (–1, –1), -√3,√3 are the vertices of an equilateral triangle.

40. Find the coordinates of the point which divides the line segment AB in the given ratio.

(i) A(5, –2,), B(9, 6), Ratio 3 : 1.
(ii) A(m + n, m – n,), B(m – n, m + n), Ratio m : n.

41. Find the coordinates of the mid points of the line segments have following end points.
(i) (–6, 5), (3, –4)
(ii) 

(iii) (a, –b), (b, –a)

ANSWER KEY

FILL IN THE BLANKS

1. 4, 3, (4, 3)

2. –3, 4, (–3, 4)

3. –5, –4, (–5, –4)

4. 3, –4, (3, –4)

MATCH THE FOLLOWING

(1 – B), (2 – A), (3 – D), (4 – G), (5 – E), (6 – C), (7 – H), (8 – F)

VERY SHORT ANSWER TYPE QUESTIONS

1. (i) B(–5, 2) (ii)C(5, –5) (iii) E (iv) G (v) 6 (vi) –3 (vii) L(0, 5) (viii) M(–3, 0)

2. (i) The x-axis and y-axis (ii)Quadrants (iii) The origin

3. (i) 2 (ii)5 (iii) (2, 5)

4. (i) –5 (ii)2 (iii) (–5, 2)

5. (i) –4 (ii)–3 (iii) (–4, –3)

6. (i) 6 (ii)–3 (iii) (6, –3)

7. (i) 1, –3, –8, 8 (ii)3, 5, –5, –7 (iii) P(1, 3), Q(–3, 5), R(–8, –5), S(8, –7)

15. (i) I quadrant (ii)II quadrant (iii) III quadrant (iv) IV quadrant.

16. Coordinates of the point P(6, 1) 17. It lies on Y-axis

SHORT ANSWER TYPE QUESTIONS

19. (i) IV quadrant (ii)III quadrant (iii) I quadrant (iv) II quadrant.

25. 20 square unit

28. ΔACD is formed.

29. Origin (0, 0)

30. III quadrant.

31. Three quadrants.

32. 5

33. √130

34. 4√2

35. 8

36. (–2, 0)

37. (0, 14)

38. AB = 65 , BC = 41 , CA = 3 10 .

40. (i) (8, 4)

41.