EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Coordinate Geometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In what ratio is the join of
(
(
−
4
)
,
(
−
1
)
)
and
(
2
,
1
)
divided by the line
(
x
−
1
)
=
0
?
(i)
5
:
1
(ii)
5
:
4
(iii)
4
:
1
(iv)
5
:
-2
(v)
6
:
1
Question
2
2.
Find the points on x-axis,
which are at a distance of
6
units
from the point
(
0
,
(
−
4
)
)
(i)
(
(
2
√
5
+
1
)
,
(
−
1
)
)
,
(
(
−
2
√
5
)
,
0
)
(ii)
(
(
2
√
5
−
2
)
,
(
−
2
)
)
,
(
(
−
2
√
5
)
,
0
)
(iii)
(
2
√
5
,
0
)
,
(
(
−
2
√
5
−
1
)
,
1
)
(iv)
(
2
√
5
,
0
)
,
(
(
−
2
√
5
)
,
0
)
(v)
(
(
2
√
5
+
2
)
,
2
)
,
(
(
−
2
√
5
)
,
0
)
Question
3
3.
A and B are two points on the x-axis and y-axis respectively.
If
(
4
,
(
−
7
)
)
is the mid-point of the join of A and B, find A and B
(i)
(
8
,
0
)
,
(
0
,
(
−
14
)
)
(ii)
(
6
,
(
−
2
)
)
,
(
0
,
(
−
14
)
)
(iii)
(
10
,
2
)
,
(
0
,
(
−
14
)
)
(iv)
(
9
,
(
−
1
)
)
,
(
0
,
(
−
14
)
)
(v)
(
8
,
0
)
,
(
(
−
1
)
,
(
−
13
)
)
Question
4
4.
A point lies on negative side of y-axis at a distance of 2 units from x-axis. What are the coordinates of the point?
(i)
(
(
−
2
)
,
0
)
(ii)
(
0
,
(
−
2
)
)
(iii)
(
0
,
2
)
(iv)
(
2
,
0
)
Question
5
5.
Find the coordinates of the mid points of the sides of the triangle formed by
(
1
,
2
)
,
(
1
,
0
)
and
(
8
,
4
)
(i)
(
0
,
2
)
,
(
9
2
,
2
)
,
(
9
2
,
3
)
(ii)
(
1
,
1
)
,
(
9
2
,
2
)
,
(
5
2
,
1
)
(iii)
(
1
,
1
)
,
(
9
2
,
2
)
,
(
9
2
,
3
)
(iv)
(
1
,
1
)
,
(
13
2
,
4
)
,
(
9
2
,
3
)
(v)
(
1
,
1
)
,
(
9
2
,
2
)
,
(
11
2
,
2
)
Question
6
6.
Find the point on x-axis which is equidistant
from the points
(
(
−
6
)
,
(
−
6
)
)
and
(
2
,
2
)
(i)
(
(
−
5
)
,
1
)
(ii)
(
(
−
4
)
,
0
)
(iii)
(
(
−
6
)
,
(
−
2
)
)
(iv)
(
(
−
2
)
,
2
)
(v)
(
(
−
3
)
,
(
−
1
)
)
Question
7
7.
A point lies on positive side of y-axis at a distance of 4 units from x-axis. What are the coordinates of the point?
(i)
(
0
,
(
−
4
)
)
(ii)
(
4
,
0
)
(iii)
(
(
−
4
)
,
0
)
(iv)
(
0
,
4
)
Question
8
8.
Find the value of k such that the points
(
(
−
7
)
,
(
−
3
)
)
,
(
61
17
,
33
17
)
and
(8,k)
are collinear
(i)
5
(ii)
1
(iii)
4
(iv)
6
(v)
3
Question
9
9.
Find the lengths of the medians of a triangle whose vertices are
(
(
−
5
)
,
(
−
3
)
)
,
(
7
,
3
)
and
(
0
,
(
−
7
)
)
(i)
1
2
√
149
,
1
2
√
41
,
3
√
5
(ii)
3
√
5
,
1
2
√
149
,
1
2
√
149
(iii)
1
2
√
293
,
1
2
√
617
,
5
√
2
Question
10
10.
In what ratio is the join of
(
5
,
9
)
and
(
(
−
6
)
,
(
−
1
)
)
divided by x-axis?
(i)
9
:
1
(ii)
8
:
0
(iii)
10
:
1
(iv)
8
:
1
(v)
8
:
5
Question
11
11.
Find the ratio in which point
(
(
−
19
13
)
,
56
13
)
divides the join of points
(
(
−
7
)
,
8
)
and
(
2
,
2
)
(i)
9
:
5
(ii)
8
:
5
(iii)
7
:
5
(iv)
8
:
7
(v)
8
:
2
Question
12
12.
The centre of a circle is
(
(
−
2
)
,
3
)
.
Find the other end of the diameter whose one end point is
(
(
−
1
)
,
5
)
(i)
(
3
,
1
)
(ii)
(
1
,
(
−
3
)
)
(iii)
(
(
−
3
)
,
1
)
(iv)
(
(
−
3
)
,
(
−
1
)
)
(v)
(
3
,
(
−
1
)
)
Question
13
13.
Find the distance between the points
(
3
,
(
−
7
)
)
and
(
5
,
5
)
(i)
2
√
34
(ii)
74
(iii)
2
√
37
(iv)
2
√
40
(v)
2
4
√
37
Question
14
14.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
6
,
3
)
and
(
2
,
(
−
2
)
)
(i)
(
8
x
+
10
y
−
37
)
=
0
(ii)
(
−
8
x
+
2
y
+
36
)
=
0
(iii)
(
−
8
x
+
4
y
+
36
)
=
0
(iv)
(
8
x
+
12
y
−
37
)
=
0
(v)
(
7
x
+
10
y
−
37
)
=
0
Question
15
15.
The points
(
(
−
2
)
,
(
−
1
)
)
,
(
4
,
(
−
4
)
)
,
(
10
,
(
−
1
)
)
and
(
4
,
2
)
represent
(i)
trapezium
(ii)
square
(iii)
parallelogram
(iv)
rhombus
(v)
rectangle
Question
16
16.
One end of the diameter of a circle is
(
4
,
7
)
.
If the centre is
(
0
,
7
2
)
,
find the other end of the diameter
(i)
(
(
−
6
)
,
(
−
2
)
)
(ii)
(
(
−
3
)
,
(
−
1
)
)
(iii)
(
(
−
5
)
,
1
)
(iv)
(
(
−
2
)
,
2
)
(v)
(
(
−
4
)
,
0
)
Question
17
17.
The points
(
(
−
3
)
,
(
−
4
)
)
,
(
3
,
(
−
4
)
)
,
(
3
,
(
−
1
)
)
and
(
(
−
3
)
,
(
−
1
)
)
represents
(i)
trapezium
(ii)
rhombus
(iii)
parallelogram
(iv)
rectangle
(v)
square
Question
18
18.
Distance of the given point from y-axis is
(i)
5
(ii)
3
(iii)
8
(iv)
-2
(v)
15
Question
19
19.
The points
(
(
−
3
)
,
(
−
3
)
)
,
(
1
,
0
)
and
(
4
,
(
−
4
)
)
represent
(i)
isosceles right angled triangle
(ii)
collinear points
(iii)
equilateral triangle
(iv)
scalene triangle
(v)
right angle triangle
Question
20
20.
The line
(
−
6
x
+
20
y
−
39
)
=
0
bisects which of the following pairs of points?
(i)
(
(
−
5
)
,
(
−
5
)
)
,
(
(
−
9
)
,
6
)
(ii)
(
(
−
3
)
,
(
−
3
)
)
,
(
(
−
8
)
,
5
)
(iii)
(
(
−
4
)
,
(
−
6
)
)
,
(
(
−
8
)
,
5
)
(iv)
(
(
−
7
)
,
(
−
7
)
)
,
(
(
−
8
)
,
5
)
(v)
(
(
−
5
)
,
(
−
5
)
)
,
(
(
−
8
)
,
5
)
Question
21
21.
Which of the following sets of points are collinear?
(i)
(
(
−
2
)
,
(
−
2
)
)
,
(
6
,
1
)
,
(
14
9
,
(
−
2
3
)
)
(ii)
(
3
,
(
−
8
)
)
,
(
(
−
5
)
,
(
−
5
)
)
,
(
8
,
4
)
(iii)
(
(
−
4
)
,
(
−
5
)
)
,
(
4
,
7
)
,
(
(
−
1
)
,
0
)
(iv)
(
(
−
6
)
,
3
)
,
(
(
−
7
)
,
(
−
1
)
)
,
(
(
−
6
)
,
1
)
(v)
(
2
,
(
−
7
)
)
,
(
8
,
1
)
,
(
5
,
2
)
Question
22
22.
Distance of the point (9,6) from y-axis is
(i)
(
−
3
)
(ii)
15
(iii)
9
(iv)
6
(v)
3
Question
23
23.
A is a point on x-axis with abscissa
(-2)
and B is a point on y-axis
with ordinate
3
.
Find the distance between A and B
(i)
√
16
(ii)
√
10
(iii)
4
√
13
(iv)
√
13
(v)
13
Question
24
24.
The points
(
(
−
5
)
,
(
−
1
)
)
,
(
(
−
2
)
,
3
)
,
(
2
,
0
)
and
(
(
−
1
)
,
(
−
4
)
)
represent
(i)
parallelogram
(ii)
trapezium
(iii)
rhombus
(iv)
rectangle
(v)
square
Question
25
25.
The points
(
(
−
4
)
,
5
)
,
(
(
−
8
)
,
(
−
8
)
)
and
(
(
−
6
+
13
2
√
3
)
,
(
−
3
2
−
2
√
3
)
)
represent
(i)
equilateral triangle
(ii)
scalene triangle
(iii)
right angled triangle
(iv)
isosceles triangle
Assignment Key
1) (i)
2) (iv)
3) (i)
4) (ii)
5) (iii)
6) (ii)
7) (iv)
8) (iii)
9) (iii)
10) (i)
11) (ii)
12) (iii)
13) (iii)
14) (i)
15) (iv)
16) (v)
17) (iv)
18) (ii)
19) (i)
20) (v)
21) (i)
22) (iii)
23) (iv)
24) (v)
25) (i)
