## 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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