Co-ordinate geometry

Mathematics (Co-ordinate geometry)

1. The point of intersection of X and Y axes is called

(a) zero point   (b) origin            (c) null point                     (d) none of these             (1)

2. The distance of the point (-3, -2) from x-axis is

(a) 2units            (b) 3units           (c) 5units            (d) 13 units       (1)

3. The distance of the point (-6, -2) from y-axis is

(a) 6units            (b) 38 units      (c) 2units            (d) 8units          (1)

4. The abscissa and ordinate of the point with Co-ordinates (8, 12) is

(A) abscissa 12 and ordinate                     (B) abscissa 8 and ordinate 12

(C) abscissa 0 and ordinate 20                   D) none of these             (1)

5. Write the name of each part of the plane formed by Vertical and horizontal lines.(2)

6. Write the Co-ordinates of a point which lies on the x-axis and is at a distance of

4units to the right of origin. Draw its graph(2)

7. Write the mirror image of the point (2, 3) and (-4, -6) with respect to x-axis. (2)

8. Write the Co-ordinates of a point which lies on y-axis and is at a distance of

3units above x-axis. Represent on the graph.(2)

9. Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (-3, 5), (-3, -5) and (6, 1) in the

Cartesian plane.(3)

10. Take a triangle ABC with A (3, 0), B (-2, 1), C (2, 1). Find its mirror image. (3)

11. In which quadrant or on which axis do each of the points (-2, 4), (2, -1), (-1, 0),

(1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane.(3)

                                                                       PART  2

1. The perpendicular bisector of a line segment AB passes through the origin. If the co-ordinates of A are (–2, 0), the co-ordinates of B are:

(a) (0, 2)         (b) (2, 0)            (c) (0, –2)                     (d) (–2, 0)

2. The point (0, 10) lies on :

(a) +ve x-axis (b) –ve x-axis           (c) +ve y-axis            (d) –ve y-axis

3. Which of the following points lies on the y-axis ?

(a) (2, 0)          (b) (0, – 4)        (c) (5, – 1)                  (d) (– 4, 0)

4. The co-ordiantes of a point are (x, y). If the point lies in the 2nd quadrant, then:

(a) x > 0, y > 0 (b) x < 0, y > 0 (c) x < 0, y < 0 (d) x > 0, y < 0

5. A point both of whose co-ordinates are negative will lie in :

(a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant

6. Points (1, –1), (2, –2), (4, –5), (–3, –4) :

(a) lie in II quadrant (b) lie in III quadrant (c) lie in IV quadrant (d) do not lie in the same quadrant

7. If y co-ordinate of a point is zero, then this point always lies :

(a) in I quadrant (b) in II quadrant (c) on x-axis (d) on y-axis

8. The points (–5, 2) and (2, –5) lie in the :

(a) Same quadrant                           (b) II and III quadrants, respectively

 (c) II and IV quadrants, respectively (d) IV and II quadrants, respectively

9. The points (other than origin) for which abscissa is equal to the ordinate will lie in :

(a) I quadrant only (b) I and II quadrants (c) I and III quadrants (d) II and IV quadrants

10. Point (–3, 5) lies in the :

(a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant

11. Signs of the abscissa and ordinate of a point in the second quadrant are respectively:

(a) +, + (b) –, – (c) –, + (d) +, –

12. Point (– 10, 0) lies :

(a) on the negative direction of the x-axis (b) on the negative direction of the y-axis (c) in the third quadrant (d) in the fourth quadrant

13. Abscissa of all the points on the x-axis is :

(a) 0 (b) 1 (c) 2 (d) any number

14. Ordinate of all points on the x-axis is :

(a) 0 (b) 1 (c) – 1 (d) any number

15. A point is at a distance of 3 units from the x-axis and 5 units from the y-axis. Which of the following may be the co-ordinates of the point ?

(a) (5, 3) (b) (–5, 3) (c) (–5, –3) (d) all the above

16. If (x + 1, 4) = (5, y – 1), then the values of x and y are :

(a) x = 4, y = 4 (b) x = 5, y = 4 (c) x = 4, y = 5 (d) x = 5, y = 5 Q. 17. Which of the following points are collinear? (a) P(0, 5), Q(5, 0),R(–5, 0) (b) A(3, 4), B(0, – 7), C(0, 8) (c) X(6, 0), Y(–10, 0), Z (0, 0) (d) L(–3, 0), M(–3, – 4), N(3, 4)

18. The point (2, 7) is at a distance of ___________ units from the y-axis.

(a) 2 (b) 7 (c) 2 + 7 (d) 7 – 2

19. The point whose ordinate is 4 and which lies on y-axis is :

(a) (4, 0) (b) (0, 4) (c) (1, 4) (d) (4, 2)

20. The perpendicular distance of the point P(3, 4) from the y-axis is :

(a) 3 (b) 4 (c) 5 (d) 7

21. The point (–5, 2) and (2, –5) lie in the:

(a) same quadrants (b) II and III quadrants respectively (c) II and IV quadrants respectively (d) IV and III quadrants respectively

22. The distance of a point (0, –3) from the origin is :

(a) 0 units (b) –3 units (c) cannot be determined (d) 3 units

23. Which of the following points lie on the negative side of x -axis?

(a) (–4, 0) (b) (–3, 2) (c) (0,–4) (d) (5, –7)

24. Ordinate of a point is negative in :

(a) III and IV quadrant (b) III quadrant only (c) II and III quadrant (d) IV quadrant only

25. The co-ordinates of the point which lies on y-axis at a distance of 4 units in negative direction of y-axis is

(a) (0, 4) (b) (4, 0) (c) (0, –4) (d) (–4, 0)

 2 Marks Questions

 1. Given point P (3, 4). What is the distance of point P from (a) x axis (b) y axis?

2. 7. Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinate of the point R such that PQRS is a square.

 3. Plot the points A (4, 0), B (4, 4) and C (0, 4) on the graph. Join OA, AB, BC, and CO. Name the figure so formed and measure its sides 4. How many axis and quadrants are there in a Cartesian plane?

 5. Plot the points on a graph paper: (a) (3, 4) (b) (-2, 3) (c) (-1,-2) (d) (5,-1)

 6. Check wheat her the points (1, 5), (0, 3) lie on the line y = 3 + 2x or not

7. Find the area of the triangle whose vertices are (0, 4), (0, 0) and (2, 0) by plotting them on graph

 8. Find the equation of a line parallel to x – axis at a distance of 2 units below x – axis

 9. Find the coordinates of the point (a) Which lies on x and y axis both (b) Whose ordinate is – 4 and which lies on y axis (c) Whose abscissa is 5 and which lies on x – axis

 10. Write the coordinates of a point left of y – axis and on y – axis at a distance of 6 units

11. Draw the graph of the equation (a)y = 3x (b) x = 4 (c) y = 5

12. A point lies on x-axis at a distance of 9 units from y-axis. What are its coordinates? What will be its coordinates if it lies on y-axis at a distance of –9 units from x-axis?

13. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular distance from the y-axis is 5 units. Write the co-ordinates of such a point if it lies in the : (a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant

14. . On the co-ordinate axes, draw a rectangle ABCD, such that its vertices are (4, 3), (4, – 2), (–7, –2) and (– 7, 3) respectively

 15. What is the perpendicular distance of the points A(7, – 4) from (i) x-axis (ii) y-axis ?

 16. In the figure, if DABC and DABD are equilateral, then find the co-ordinates of points C and D.

17. Mark the points (0, 2), (3, 0), (–3, 0) and (0, –2) on a graph. Join these points. Name the figure obtained and find the area of the figure so obtained.

18. In fig, ABC is a triangle with co-ordinates of A and O as (4, 0) and (0, 0) respectively. AB = 5. Find the co-ordinates of B.

19. Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.

20. Find the point where the line represented by the equation 5y – 3x – 10 = 0 cuts the y-axis.

                                             PART  3

1. In which quadrant or on which axes do each point lies

 a) The ordinate is 3 and abscissa is – 4                                 b) The abscissa is – 2 and ordinate is – 3

 c) (- 3, 2)                    d) (0, - 4)                     e) (5, 0)

 2. Given point P (3, 4). What is the distance of point P from (a) x axis (b) y axis?

 3. Plot the points A (4, 0), B (4, 4) and C (0, 4) on the graph. Join OA, AB, BC, and CO. Name the figure so formed and measure its sides

 4. How many axis and quadrants are there in a Cartesian plane?

 5. Plot the points on a graph paper: (a) (3, 4) (b) (-2, 3) (c) (-1,-2) (d) (5,-1)

6. Check wheat her the points (1, 5), (0, 3) lie on the line y = 3 + 2x or not

 7. Find the area of the triangle whose vertices are (0, 4), (0, 0) and (2, 0) by plotting them on graph

8. Find the equation of a line parallel to x – axis at a distance of 2 units below x - axis

9. Find the coordinates of the point (a) Which lies on x and y axis both (b) Whose ordinate is – 4 and which lies on y axis (c) Whose abscissa is 5 and which lies on x – axis

 10. Write the coordinates of a point left of y – axis and on y – axis at a distance of 6 units

11. Draw the graph of the equation y = 3x

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