EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Find the point that bisects
(
5
,
(
−
4
)
)
and
(
(
−
1
)
,
3
)
(i)
(
0
,
(
−
5
2
)
)
(ii)
(
1
,
1
2
)
(iii)
(
4
,
3
2
)
(iv)
(
2
,
(
−
1
2
)
)
(v)
(
3
,
(
−
3
2
)
)
Question
2
2.
The mid-point of the join of points
(
2
,
5
)
and
(
8
,
(
−
7
)
)
is
(i)
(
5
,
(
−
1
)
)
(ii)
(
6
,
(
−
2
)
)
(iii)
(
3
,
(
−
3
)
)
(iv)
(
4
,
0
)
(v)
(
7
,
1
)
Question
3
3.
Find the point on y-axis which is equidistant
from the points
(
(
−
5
)
,
6
)
and
(
0
,
(
−
5
)
)
(i)
(
2
,
40
11
)
(ii)
(
(
−
1
)
,
29
11
)
(iii)
(
(
−
2
)
,
(
−
4
11
)
)
(iv)
(
0
,
18
11
)
(v)
(
1
,
7
11
)
Question
4
4.
Find the area of the triangle
formed by the points
(
4
,
(
−
8
)
)
,
(
(
−
6
)
,
(
−
6
)
)
and
(
(
−
3
)
,
6
)
(i)
64
(ii)
65
(iii)
63
(iv)
62
(v)
60
Question
5
5.
In what ratio is the join of
(
(
−
7
)
,
2
)
and
(
2
,
(
−
5
)
)
divided by the line
(
x
+
1
)
=
0
?
(i)
6
:
3
(ii)
6
:
5
(iii)
7
:
3
(iv)
6
:
1
(v)
5
:
3
Question
6
6.
Distance of the given point from x-axis is
(i)
4
(ii)
0
(iii)
2
Question
7
7.
One end of the diameter of a circle is
(
6
,
0
)
.
If the centre is
(
2
,
(
−
3
)
)
,
find the other end of the diameter
(i)
(
(
−
2
)
,
(
−
6
)
)
(ii)
(
(
−
1
)
,
(
−
7
)
)
(iii)
(
(
−
3
)
,
(
−
5
)
)
(iv)
(
0
,
(
−
4
)
)
(v)
(
(
−
4
)
,
(
−
8
)
)
Question
8
8.
Find the coordinates of the points of trisection of the line segment
joining the points
(
(
−
1
)
,
(
−
7
)
)
and
(
6
,
4
)
(i)
(
(
−
2
3
)
,
(
−
16
3
)
)
,
(
11
3
,
1
3
)
(ii)
(
7
3
,
(
−
13
3
)
)
,
(
11
3
,
1
3
)
(iii)
(
4
3
,
(
−
10
3
)
)
,
(
11
3
,
1
3
)
(iv)
(
4
3
,
(
−
10
3
)
)
,
(
8
3
,
4
3
)
(v)
(
10
3
,
(
−
4
3
)
)
,
(
11
3
,
1
3
)
Question
9
9.
Find the radius of the circle passing through the points
(
(
−
2
)
,
(
−
3
)
)
,
(
(
−
6
)
,
(
−
7
)
)
and
(
7
,
4
)
(i)
5
2
√
751
(ii)
1885
(iii)
5
2
4
√
754
(iv)
5
2
√
757
(v)
5
2
√
754
Question
10
10.
If point P
(
0
,
4
)
bisects A
(
1
,
4
)
and B
(
x
,
y
)
, find
(
x
,
y
)
(i)
(
(
−
2
)
,
5
)
(ii)
(
0
,
3
)
(iii)
(
(
−
1
)
,
4
)
(iv)
(
(
−
3
)
,
2
)
(v)
(
1
,
6
)
Question
11
11.
The points
(
(
−
7
)
,
(
−
7
)
)
,
(
7
,
2
)
and
(
243
34
,
(
−
463
34
)
)
represent
(i)
isosceles triangle
(ii)
equilateral triangle
(iii)
right angle triangle
(iv)
collinear points
(v)
scalene triangle
Question
12
12.
Determine the ratio in which the line
(
6
x
−
8
y
+
30
)
=
0
divides the join of points
(
5
,
(
−
2
)
)
and
(
(
−
2
)
,
5
)
(i)
38
:
11
(ii)
38
:
13
(iii)
37
:
11
(iv)
38
:
8
(v)
39
:
11
Question
13
13.
The points
(
(
−
5
)
,
8
)
,
(
5
,
(
−
8
)
)
and
(
5
19
,
(
−
8
19
)
)
represents
(i)
collinear points
(ii)
right angle triangle
(iii)
isoceles triangle
(iv)
equilateral triangle
Question
14
14.
A point lies on negative side of x-axis at a distance of 4 units from y-axis. What are the coordinates of the point?
(i)
(
4
,
0
)
(ii)
(
0
,
4
)
(iii)
(
(
−
4
)
,
0
)
(iv)
(
0
,
(
−
4
)
)
Question
15
15.
The points
(
(
−
4
)
,
(
−
1
)
)
,
(
0
,
3
)
,
(
4
,
(
−
1
)
)
and
(
0
,
(
−
5
)
)
represent
(i)
rhombus
(ii)
parallelogram
(iii)
square
(iv)
trapezium
(v)
rectangle
Question
16
16.
Find the points on x-axis,
which are at a distance of
7
units
from the point
(
8
,
(
−
1
)
)
(i)
(
(
10
+
4
√
3
)
,
2
)
,
(
(
8
−
4
√
3
)
,
0
)
(ii)
(
(
8
+
4
√
3
)
,
0
)
,
(
(
7
−
4
√
3
)
,
1
)
(iii)
(
(
9
+
4
√
3
)
,
(
−
1
)
)
,
(
(
8
−
4
√
3
)
,
0
)
(iv)
(
(
6
+
4
√
3
)
,
(
−
2
)
)
,
(
(
8
−
4
√
3
)
,
0
)
(v)
(
(
8
+
4
√
3
)
,
0
)
,
(
(
8
−
4
√
3
)
,
0
)
Question
17
17.
KM is the straight line of length
√
2
units.
If K has the coordinates
(
1
,
3
)
and M has coordinates
(k,4)
,
find the possible values of k
(i)
(
4
,
2
)
(ii)
(
0
,
(
−
2
)
)
(iii)
(
3
,
(
−
1
)
)
(iv)
(
1
,
1
)
(v)
(
2
,
0
)
Question
18
18.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
4
,
(
−
3
)
)
and
(
7
,
5
)
(i)
(
6
x
+
16
y
−
49
)
=
0
(ii)
(
6
x
+
18
y
−
49
)
=
0
(iii)
(
7
x
−
4
y
−
31
)
=
0
(iv)
(
5
x
+
16
y
−
49
)
=
0
(v)
(
7
x
−
y
−
31
)
=
0
Question
19
19.
Find the point that divides the join of points
(
2
,
(
−
6
)
)
and
(
(
−
1
)
,
4
)
internally
in the ratio
6
:
7
(i)
(
(
−
18
13
)
,
(
−
44
13
)
)
(ii)
(
(
−
5
13
)
,
(
−
5
13
)
)
(iii)
(
34
13
,
8
13
)
(iv)
(
21
13
,
(
−
31
13
)
)
(v)
(
8
13
,
(
−
18
13
)
)
Question
20
20.
In what ratio is the join of
(
(
−
3
)
,
(
−
2
)
)
and
(
(
−
2
)
,
7
)
divided by the line
(
−
y
+
2
)
=
0
?
(i)
5
:
5
(ii)
3
:
5
(iii)
4
:
2
(iv)
4
:
5
(v)
4
:
7
Question
21
21.
Distance of the point (2,9) from x-axis is
(i)
11
(ii)
2
(iii)
9
(iv)
(
−
7
)
(v)
7
Question
22
22.
A point lies on positive side of x-axis at a distance of 6 units from y-axis. What are the coordinates of the point?
(i)
(
0
,
(
−
6
)
)
(ii)
(
0
,
6
)
(iii)
(
(
−
6
)
,
0
)
(iv)
(
6
,
0
)
Question
23
23.
Find the distance of the point
(
(
−
3
)
,
8
)
from origin
(i)
√
73
(ii)
4
√
73
(iii)
73
(iv)
√
70
(v)
√
76
Question
24
24.
Find the centre of the circle, the endpoints of whose
diameter are
(
3
,
0
)
and
(
3
,
(
−
1
)
)
(i)
(
(
−
3
)
,
1
2
)
(ii)
(
3
,
1
2
)
(iii)
(
(
−
3
)
,
(
−
1
2
)
)
(iv)
(
3
,
(
−
1
2
)
)
(v)
(
(
−
1
2
)
,
3
)
Question
25
25.
Find the value of k such that the points
(
(
−
9
)
,
(
−
6
)
)
,
(
(
−
19
5
)
,
0
)
and
(4,k)
are collinear
(i)
7
(ii)
10
(iii)
8
(iv)
9
(v)
11
Assignment Key
1) (iv)
2) (i)
3) (iv)
4) (iii)
5) (i)
6) (iii)
7) (i)
8) (iii)
9) (v)
10) (iii)
11) (i)
12) (i)
13) (i)
14) (iii)
15) (iii)
16) (v)
17) (v)
18) (i)
19) (v)
20) (iv)
21) (iii)
22) (iv)
23) (i)
24) (iv)
25) (iv)
