EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Find the radius of the circle passing through the points
(
(
−
2
)
,
(
−
3
)
)
,
(
6
,
1
)
and
(
5
,
1
)
(i)
65
2
(ii)
5
2
√
15
(iii)
5
2
4
√
13
(iv)
5
2
√
13
(v)
5
2
√
10
Question
2
2.
The centre of a circle is
(
5
2
,
(
−
11
2
)
)
.
Find the other end of the diameter whose one end point is
(
(
−
3
)
,
(
−
3
)
)
(i)
(
8
,
(
−
8
)
)
(ii)
(
8
,
8
)
(iii)
(
(
−
8
)
,
(
−
8
)
)
(iv)
(
(
−
8
)
,
8
)
Question
3
3.
One end of the diameter of a circle is
(
(
−
7
)
,
4
)
.
If the centre is
(
(
−
3
)
,
3
)
,
find the other end of the diameter
(i)
(
1
,
2
)
(ii)
(
(
−
1
)
,
0
)
(iii)
(
0
,
3
)
(iv)
(
3
,
4
)
(v)
(
2
,
1
)
Question
4
4.
Find the value of k such that the points
(
(
−
7
)
,
(
−
5
)
)
,
(
(
−
4
)
,
(
−
9
4
)
)
and
(k,6)
are collinear
(i)
4
(ii)
2
(iii)
6
(iv)
8
(v)
5
Question
5
5.
Find the centroid of the triangle formed by the points
(
4
,
2
)
,
(
(
−
2
)
,
(
−
8
)
)
and
(
(
−
6
)
,
7
)
(i)
(
(
−
10
3
)
,
(
−
5
3
)
)
(ii)
(
(
−
1
3
)
,
(
−
2
3
)
)
(iii)
(
(
−
4
3
)
,
1
3
)
(iv)
(
(
−
7
3
)
,
4
3
)
(v)
(
2
3
,
7
3
)
Question
6
6.
The points
(
(
−
6
)
,
(
−
6
)
)
,
(
2
,
(
−
6
)
)
,
(
4
,
(
−
1
)
)
and
(
(
−
4
)
,
(
−
1
)
)
represent
(i)
parallelogram
(ii)
square
(iii)
rectangle
(iv)
trapezium
(v)
rhombus
Question
7
7.
Find the lengths of the medians of a triangle whose vertices are
(
3
,
6
)
,
(
(
−
1
)
,
(
−
4
)
)
and
(
7
,
6
)
(i)
√
41
,
2
,
√
29
(ii)
√
29
,
√
41
,
√
41
(iii)
5
,
2
√
34
,
√
61
Question
8
8.
Determine the ratio in which the line
(
2
x
−
10
y
+
42
)
=
0
divides the join of points
(
2
,
(
−
3
)
)
and
(
3
,
7
)
(i)
38
:
11
(ii)
38
:
14
(iii)
37
:
11
(iv)
39
:
11
(v)
38
:
8
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)
(
n
x
2
−
m
x
1
m - n
,
n
y
2
−
m
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)
(
m
x
2
−
n
x
1
m - n
,
m
y
2
−
n
y
1
m - n
)
Question
10
10.
A point lies on positive side of x-axis at a distance of 3 units from y-axis. What are the coordinates of the point?
(i)
(
0
,
3
)
(ii)
(
(
−
3
)
,
0
)
(iii)
(
3
,
0
)
(iv)
(
0
,
(
−
3
)
)
Question
11
11.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
2
,
4
)
and
(
6
,
(
−
5
)
)
(i)
(
−
9
x
+
18
y
+
41
)
=
0
(ii)
(
−
8
x
+
20
y
+
41
)
=
0
(iii)
(
−
7
x
+
14
)
=
0
(iv)
(
−
7
x
+
11
)
=
0
(v)
(
−
8
x
+
18
y
+
41
)
=
0
Question
12
12.
The points
(
1
,
(
−
5
)
)
,
(
(
−
4
)
,
(
−
2
)
)
and
(
(
−
3
2
−
3
2
√
3
)
,
(
−
7
2
−
5
2
√
3
)
)
represent
(i)
right angled triangle
(ii)
equilateral triangle
(iii)
scalene triangle
(iv)
isosceles triangle
Question
13
13.
Two vertices of a triangle are
(
1
,
6
)
,
(
(
−
6
)
,
(
−
6
)
)
and its centriod is
(
(
−
5
3
)
,
(
−
2
3
)
)
. Find the coordinates of the third vertex of the triangle
(i)
(
(
−
2
)
,
0
)
(ii)
(
0
,
2
)
(iii)
(
0
,
(
−
2
)
)
Question
14
14.
The centroid of the triangle formed by the points
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
and
(
x
3
,
y
3
)
is
(i)
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
)
(ii)
(
x
1
−
x
2
−
x
3
3
,
y
1
−
y
2
−
y
3
3
)
(iii)
(
y
1
+
y
2
+
y
3
2
,
x
1
+
x
2
+
x
3
2
)
(iv)
(
x
1
−
x
2
−
x
3
2
,
y
1
−
y
2
−
y
3
2
)
(v)
(
y
1
−
y
2
−
y
3
2
,
x
1
−
x
2
−
x
3
2
)
Question
15
15.
Find the value of k such that the points
(
(
−
8
)
,
(
−
2
)
)
,
(
(
−
44
9
)
,
2
3
)
and
(-1,k)
are collinear
(i)
4
(ii)
5
(iii)
3
(iv)
6
(v)
1
Question
16
16.
If point P
(
22
9
,
3
)
is equidistant from the points
(a,3)
and
(
(
−
2
)
,
4
)
, find a
(i)
6
(ii)
7
(iii)
5
(iv)
8
(v)
10
Question
17
17.
Find the area of the quadrilateral formed by
(
(
−
1
)
,
(
−
8
)
)
,
(
5
,
(
−
3
)
)
,
(
(
−
1
)
,
0
)
and
(
(
−
2
)
,
(
−
1
)
)
(i)
27
(ii)
28
(iii)
31
(iv)
29
(v)
26
Question
18
18.
If A
(
8
,
(
−
4
)
)
and B
(
0
,
2
)
are two points,
find the coordinates of the point C on AB produced so that AC = 2BC
(i)
(
(
−
9
)
,
9
)
(ii)
(
(
−
7
)
,
7
)
(iii)
(
(
−
10
)
,
6
)
(iv)
(
(
−
6
)
,
10
)
(v)
(
(
−
8
)
,
8
)
Question
19
19.
Distance of the given point from y-axis is
(i)
12
(ii)
2
(iii)
5
(iv)
35
(v)
7
Question
20
20.
Distance of the given point from x-axis is
(i)
-2
(ii)
3
(iii)
4
(iv)
1
Question
21
21.
Find the lengths of the sides of the triangle formed by the points
(
(
−
8
)
,
(
−
2
)
)
,
(
2
,
(
−
4
)
)
and
(
(
−
1
)
,
1
)
(i)
2
√
26
,
√
34
,
√
60
(ii)
2
4
√
26
,
√
34
,
√
58
(iii)
2
√
26
,
34
,
√
58
(iv)
2
√
26
,
√
34
,
√
58
Question
22
22.
If point P
(
1
,
(
−
7
)
)
bisects A
(
2
,
(
−
7
)
)
and B
(
x
,
y
)
, find
(
x
,
y
)
(i)
(
(
−
1
)
,
(
−
6
)
)
(ii)
(
0
,
(
−
7
)
)
(iii)
(
(
−
2
)
,
(
−
9
)
)
(iv)
(
1
,
(
−
8
)
)
(v)
(
2
,
(
−
5
)
)
Question
23
23.
If point P
(x,7)
is equidistant from the points
(
2
,
6
)
and
(
4
,
1
)
, find x
(i)
23
2
(ii)
45
4
(iii)
49
4
(iv)
25
2
(v)
47
4
Question
24
24.
Find the ratio in which point
(
(
−
4
5
)
,
18
5
)
divides the join of points
(
(
−
5
)
,
3
)
and
(
2
,
4
)
(i)
9
:
4
(ii)
8
:
6
(iii)
9
:
9
(iv)
10
:
6
(v)
9
:
6
Question
25
25.
Find the point which is equidistant from the points
(
5
,
(
−
3
)
)
,
(
(
−
8
)
,
(
−
2
)
)
and
(
(
−
2
)
,
8
)
(i)
(
(
−
9
4
)
,
7
4
)
(ii)
(
3
4
,
11
4
)
(iii)
(
(
−
5
4
)
,
3
4
)
(iv)
(
(
−
1
4
)
,
(
−
1
4
)
)
(v)
(
(
−
13
4
)
,
(
−
5
4
)
)
Assignment Key
1) (iv)
2) (i)
3) (i)
4) (v)
5) (iii)
6) (i)
7) (iii)
8) (i)
9) (iii)
10) (iii)
11) (v)
12) (ii)
13) (iii)
14) (i)
15) (i)
16) (ii)
17) (ii)
18) (v)
19) (v)
20) (iv)
21) (iv)
22) (ii)
23) (v)
24) (v)
25) (iii)
