Coordinate Geometry - Important Question Paper

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50

    Part A

    15 x 1 = 15
  1. Point (–3,5) lie in the ________ quadrant

    (a)

    I

    (b)

    II 

    (c)

    III 

    (d)

    IV 

  2. Signs of the abscissa and ordinate of a point in the fourth quadrant are respectively

    (a)

    (+,+)

    (b)

    ( –, –)

    (c)

    (–, +)

    (d)

    ( +, –)

  3. On plotting the points O(0,0), A(3, – 4), B(3, 4) and C(0, 4) and joining OA, AB, BC and CO, which of the following figure is obtained?

    (a)

    Square

    (b)

    Rectangle

    (c)

    Trapezium

    (d)

    Rhombus

  4. If P( –1,1), Q( 3,–4), R( 1, –1), S(–2, –3) and T( –4, 4) are plotted on a graph paper, then the points in the fourth quadrant are

    (a)

    P and T

    (b)

    Q and R

    (c)

    only S

    (d)

    P and Q

  5. The point whose ordinate is 4 and which lies on the y-axis is............

    (a)

    ( 4, 0 )

    (b)

    (0, 4)

    (c)

    (1, 4)

    (d)

    (4, 2)

  6. The distance between the two points ( 2, 3 ) and ( 1, 4 ) is ______

    (a)

    2

    (b)

    \(\sqrt { 56 } \)

    (c)

    \(\sqrt { 10 } \)

    (d)

    \(\sqrt { 2 } \)

  7. If the points A (2,0), B (-6,0), C (3, a–3) lie on the x-axis then the value of a is _____

    (a)

    0

    (b)

    2

    (c)

    3

    (d)

    -6

  8. If ( x+2, 4) = (5, y–2), then the coordinates (x,y) are _____

    (a)

    (7, 12)

    (b)

    (6, 3)

    (c)

    (3, 6)

    (d)

    (2, 1)

  9. If Q1,Q2, Q3, Q4 are the quadrants in a Cartesian plane then \({ Q }_{ 2 }\cap { Q }_{ 3 }\)

    (a)

    \({ Q }_{ 1 }\cup { Q }_{ 2 }\)

    (b)

    \({ Q }_{ 2 }\cup { Q }_{ 3 }\)

    (c)

    Null set

    (d)

    Negative x-axis

  10. The distance between the point ( 5, –1 ) and the origin is _________

    (a)

    \(\sqrt { 24 } \)

    (b)

    \(\sqrt { 37 } \)

    (c)

    \(\sqrt { 26 } \)

    (d)

    \(\sqrt { 17 } \)

  11. On which quadrant does the point (- 4, 3) lie?

    (a)

    I

    (b)

    II

    (c)

    III

    (d)

    IV

  12. The point whose abscissa is 5 and lies on the x-axis is__________

    (a)

    (-5, 0)

    (b)

    (5,5)

    (c)

    (0,5)

    (d)

    (5,0)

  13. A point which lies in the III quadrant is__________________

    (a)

    (5, 4)

    (b)

    (5, - 4)

    (c)

    (-5, - 4)

    (d)

    (-5,4)

  14. A point on the y-axis is ________________

    (a)

    (1, 1)

    (b)

    (6,0)

    (c)

    (0,6)

    (d)

    (-1, -1)

  15. The centre of a circle is (0, 0). One end point of a diameter is (5, -1), then ______________

    (a)

    \(\sqrt{24}\)

    (b)

    \(\sqrt{37}\)

    (c)

    \(\sqrt{26}\)

    (d)

    \(\sqrt{17}\)

  16. Part B

    5 x 2 = 10
  17. Plot the following points in the coordinate plane and join them. What is your conclusion about the resulting figure? (0,–4) (0,–2) (0,4) (0,5)

  18. Plot the following points in the coordinate plane. Join them in order. What type of geometrical shape is formed? (0,0) (–4,0) (–4,–4) (0,–4)

  19. Plot the following points in the coordinate plane. Join them in order. What type of geometrical shape is formed? (–3,3) (2,3) (–6,–1) (5,–1)

  20. Find the distance between the following pairs of points. (3,– 9) and (–2, 3)

  21. Plot the points A( -1,0), B( 3, 0), C(3, 4), and 0(-1, 4) on a graph sheet. Join them to form a rectangle. Draw the mirror image Of the diagram in clockwise direction:
    (i) about x-axis. (ii) about y-axis.
    What is your observation on the coordinates of the mirror image?

  22. Part C

    5 x 3 = 15
  23. Show that the following points A(3,1) , B(6,4) and C(8,6) lies on a straight line

  24. Calculate the distance between the points A (7, 3) and B which lies on the x-axis whose abscissa is 11.

  25. The point (x, y) is equidistant from the points (3,4)and(–5,6). Find a relation between x and y.

  26. Let A(2, 3) and B(2,–4) be two points. If P lies on the x-axis, such that AP = \(\frac{3}{7}\) AB, find the coordinates of P.

  27. Find the perimeter of the triangle whose vertices are(3,2), (7,2) and (7, 5).

  28. Part D

    2 x 5 = 10
  29. Show that the point (3, -2), (3, 2), (-1, 2) and (-1, -2) taken in order are the vertices of a square.

  30. Show that the point A (3,7) B (6, 5) and C (15, -1) are collinear.

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