EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The mid-point of the join of the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is
(i)
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(ii)
(
y
1
−
y
2
2
,
x
1
−
x
2
2
)
(iii)
(
x
1
+
x
2
3
,
y
1
+
y
2
3
)
(iv)
(
x
1
−
x
2
3
,
y
1
−
y
2
3
)
(v)
(
x
1
−
x
2
2
,
y
1
−
y
2
2
)
Question
2
2.
Find the circumradius of the triangle whose vertices are
(
(
−
3
)
,
8
)
,
(
5
,
8
)
and
(
(
−
5
)
,
(
−
6
)
)
(i)
10
7
√
37
(ii)
10
7
√
39
(iii)
10
7
√
34
(iv)
370
7
(v)
10
7
4
√
37
Question
3
3.
If A
(
(
−
8
)
,
4
)
and B
(
2
,
(
−
8
)
)
are two points,
find the coordinates of the point C on AB produced so that AC = 2BC
(i)
(
12
,
(
−
20
)
)
(ii)
(
13
,
(
−
21
)
)
(iii)
(
11
,
(
−
19
)
)
(iv)
(
14
,
(
−
18
)
)
(v)
(
10
,
(
−
22
)
)
Question
4
4.
Which of the following sets of points are collinear?
(i)
(
(
−
7
)
,
2
)
,
(
6
,
6
)
,
(
(
−
7
)
,
(
−
7
)
)
(ii)
(
3
,
0
)
,
(
0
,
4
)
,
(
21
5
,
(
−
8
5
)
)
(iii)
(
(
−
7
)
,
(
−
8
)
)
,
(
8
,
(
−
1
)
)
,
(
3
,
2
)
(iv)
(
(
−
8
)
,
7
)
,
(
(
−
6
)
,
(
−
6
)
)
,
(
4
,
6
)
(v)
(
6
,
(
−
4
)
)
,
(
3
,
(
−
4
)
)
,
(
3
,
(
−
2
)
)
Question
5
5.
A point lies on negative side of y-axis at a distance of 8 units from x-axis. What are the coordinates of the point?
(i)
(
0
,
(
−
8
)
)
(ii)
(
8
,
0
)
(iii)
(
(
−
8
)
,
0
)
(iv)
(
0
,
8
)
Question
6
6.
Find the point which is equidistant from the points
(
0
,
6
)
,
(
6
,
3
)
and
(
(
−
6
)
,
(
−
2
)
)
(i)
(
(
−
6
11
)
,
9
22
)
(ii)
(
16
11
,
(
−
35
22
)
)
(iii)
(
5
11
,
(
−
13
22
)
)
(iv)
(
27
11
,
31
22
)
(v)
(
(
−
17
11
)
,
(
−
57
22
)
)
Question
7
7.
Find the radius of the circle passing through the points
(
4
,
1
)
,
(
(
−
3
)
,
6
)
and
(
2
,
6
)
(i)
1
10
√
2146
(ii)
1
10
√
2149
(iii)
1
10
4
√
2146
(iv)
1073
5
(v)
1
10
√
2143
Question
8
8.
If point P
(
27
2
,
2
)
is equidistant from the points
(a,-4)
and
(
3
,
6
)
, find a
(i)
1
(ii)
5
(iii)
3
(iv)
4
(v)
7
Question
9
9.
The coordinates of the point dividing the join of points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
internally in the ratio m:n are
(i)
(
m
x
2
+
n
x
1
m + n
,
m
y
2
+
n
y
1
m + n
)
(ii)
(
n
x
2
−
m
x
1
m - n
,
n
y
2
−
m
y
1
m - n
)
(iii)
(
m
x
2
−
n
x
1
m - n
,
m
y
2
−
n
y
1
m - n
)
(iv)
(
n
x
2
+
m
x
1
m + n
,
n
y
2
+
m
y
1
m + n
)
Question
10
10.
The points
(
7
,
4
)
,
(
(
−
7
)
,
(
−
4
)
)
and
(
(
−
21
8
)
,
(
−
3
2
)
)
represents
(i)
collinear points
(ii)
isoceles triangle
(iii)
equilateral triangle
(iv)
right angle triangle
Question
11
11.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
5
,
7
)
and
(
(
−
5
)
,
(
−
7
)
)
(i)
(
4
x
+
7
y
)
=
0
(ii)
(
−
11
x
+
10
y
−
15
)
=
0
(iii)
(
−
11
x
+
8
y
−
15
)
=
0
(iv)
(
5
x
+
7
y
)
=
0
(v)
(
5
x
+
9
y
)
=
0
Question
12
12.
Find the points on x-axis,
which are at a distance of
7
units
from the point
(
(
−
8
)
,
5
)
(i)
(
(
−
8
+
2
√
6
)
,
0
)
,
(
(
−
8
−
2
√
6
)
,
0
)
(ii)
(
(
−
7
+
2
√
6
)
,
(
−
1
)
)
,
(
(
−
8
−
2
√
6
)
,
0
)
(iii)
(
(
−
8
+
2
√
6
)
,
0
)
,
(
(
−
9
−
2
√
6
)
,
1
)
(iv)
(
(
−
6
+
2
√
6
)
,
2
)
,
(
(
−
8
−
2
√
6
)
,
0
)
(v)
(
(
−
10
+
2
√
6
)
,
(
−
2
)
)
,
(
(
−
8
−
2
√
6
)
,
0
)
Question
13
13.
Find the centre of the circle passing through
the points
(
(
−
8
)
,
(
−
2
)
)
,
(
1
,
1
)
and
(
(
−
3
)
,
2
)
(i)
(
(
−
5
14
)
,
(
−
27
14
)
)
(ii)
(
(
−
47
14
)
,
(
−
41
14
)
)
(iii)
(
(
−
19
14
)
,
(
−
69
14
)
)
(iv)
(
(
−
61
14
)
,
(
−
83
14
)
)
(v)
(
(
−
33
14
)
,
(
−
55
14
)
)
Question
14
14.
Find the relation between x and y if the points
(
x
,
y
)
,
(
5
,
(
−
2
)
)
and
(
(
−
6
)
,
(
−
3
)
)
are collinear
(i)
(
−
x
+
5
)
=
0
(ii)
(
4
x
−
5
y
+
9
)
=
0
(iii)
(
−
x
+
11
y
+
27
)
=
0
(iv)
(
−
11
y
−
33
)
=
0
(v)
(
4
x
+
6
y
−
2
)
=
0
Question
15
15.
Find the value of k such that the points
(
(
−
5
)
,
(
−
7
)
)
,
(
(
−
83
13
)
,
2
)
and
(-7,k)
are collinear
(i)
9
(ii)
6
(iii)
4
(iv)
7
(v)
5
Question
16
16.
The points B
(
(
−
1
)
,
7
)
and D
(
(
−
8
)
,
6
)
are the opposite vertices
of a square ABCD. Find the other two vertices
(i)
(
(
−
3
)
,
2
)
,
(
(
−
5
)
,
10
)
(ii)
(
(
−
4
)
,
3
)
,
(
(
−
5
)
,
10
)
(iii)
(
(
−
4
)
,
3
)
,
(
(
−
6
)
,
11
)
(iv)
(
(
−
2
)
,
5
)
,
(
(
−
5
)
,
10
)
(v)
(
(
−
6
)
,
1
)
,
(
(
−
5
)
,
10
)
Question
17
17.
Find the points on y-axis,
which are at a distance of
4
units
from the point
(
(
−
3
)
,
(
−
5
)
)
(i)
(
1
,
(
−
6
+
√
7
)
)
,
(
0
,
(
−
5
−
√
7
)
)
(ii)
(
(
−
2
)
,
(
−
7
+
√
7
)
)
,
(
0
,
(
−
5
−
√
7
)
)
(iii)
(
0
,
(
−
5
+
√
7
)
)
,
(
(
−
1
)
,
(
−
4
−
√
7
)
)
(iv)
(
2
,
(
−
3
+
√
7
)
)
,
(
0
,
(
−
5
−
√
7
)
)
(v)
(
0
,
(
−
5
+
√
7
)
)
,
(
0
,
(
−
5
−
√
7
)
)
Question
18
18.
Find the lengths of the sides of the triangle formed by the points
(
1
,
5
)
,
(
0
,
6
)
and
(
(
−
5
)
,
0
)
(i)
4
√
2
,
√
61
,
√
61
(ii)
√
2
,
61
,
√
61
(iii)
√
2
,
√
61
,
√
61
(iv)
√
2
,
√
61
,
√
64
Question
19
19.
Find the coordinates of the points of trisection of the line segment
joining the points
(
(
−
6
)
,
0
)
and
(
(
−
5
)
,
3
)
(i)
(
(
−
11
3
)
,
3
)
,
(
(
−
16
3
)
,
2
)
(ii)
(
(
−
17
3
)
,
1
)
,
(
(
−
19
3
)
,
3
)
(iii)
(
(
−
23
3
)
,
(
−
1
)
)
,
(
(
−
16
3
)
,
2
)
(iv)
(
(
−
17
3
)
,
1
)
,
(
(
−
16
3
)
,
2
)
(v)
(
(
−
14
3
)
,
0
)
,
(
(
−
16
3
)
,
2
)
Question
20
20.
If the point
(
(
−
11
2
)
,
39
7
)
divides the join of points
(
(
−
1
)
,
3
)
and
(
x
,
y
)
in the ratio
9
:
5
, find
(
x
,
y
)
(i)
(
(
−
6
)
,
9
)
(ii)
(
(
−
10
)
,
5
)
(iii)
(
(
−
9
)
,
8
)
(iv)
(
(
−
8
)
,
7
)
(v)
(
(
−
7
)
,
6
)
Question
21
21.
If point P
(x,6)
is equidistant from the points
(
(
−
8
)
,
(
−
7
)
)
and
(
(
−
7
)
,
2
)
, find x
(i)
-83
(ii)
-82
(iii)
-87
(iv)
-84
(v)
-85
Question
22
22.
Find the perimeter of the triangle formed by the points
(
(
−
6
)
,
(
−
6
)
)
,
(
2
,
7
)
and
(
3
,
(
−
2
)
)
(i)
(
√
233
+
√
84
+
√
97
)
(ii)
(
√
233
+
√
82
+
4
√
97
)
(iii)
(
√
233
+
√
82
+
√
97
)
(iv)
(
√
233
+
√
79
+
√
97
)
(v)
(
√
233
+
√
82
+
97
)
Question
23
23.
Find the centre of the circle, the endpoints of whose
diameter are
(
(
−
5
)
,
(
−
2
)
)
and
(
0
,
(
−
1
)
)
(i)
(
5
2
,
(
−
3
2
)
)
(ii)
(
(
−
5
2
)
,
(
−
3
2
)
)
(iii)
(
5
2
,
3
2
)
(iv)
(
(
−
3
2
)
,
(
−
5
2
)
)
(v)
(
(
−
5
2
)
,
3
2
)
Question
24
24.
Distance of the given point from x-axis is
(i)
10
(ii)
6
(iii)
8
(iv)
16
(v)
2
Question
25
25.
The centre of a circle is
(
(
−
1
2
)
,
(
−
4
)
)
.
Find the other end of the diameter whose one end point is
(
3
,
(
−
2
)
)
(i)
(
(
−
6
)
,
(
−
4
)
)
(ii)
(
(
−
4
)
,
6
)
(iii)
(
(
−
4
)
,
(
−
6
)
)
(iv)
(
4
,
(
−
6
)
)
(v)
(
4
,
6
)
Assignment Key
1) (i)
2) (i)
3) (i)
4) (ii)
5) (i)
6) (iii)
7) (i)
8) (iv)
9) (i)
10) (i)
11) (iv)
12) (i)
13) (v)
14) (iii)
15) (ii)
16) (ii)
17) (v)
18) (iii)
19) (iv)
20) (iv)
21) (iv)
22) (iii)
23) (ii)
24) (iii)
25) (iii)
