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 divides the join of points
(
(
−
2
)
,
0
)
and
(
(
−
7
)
,
1
)
internally
in the ratio
6
:
9
(i)
(
(
−
3
)
,
(
−
3
5
)
)
(ii)
(
(
−
6
)
,
(
−
8
5
)
)
(iii)
(
(
−
5
)
,
7
5
)
(iv)
(
(
−
2
)
,
12
5
)
(v)
(
(
−
4
)
,
2
5
)
Question
2
2.
Distance of the point (4,2) from x-axis is
(i)
6
(ii)
2
(iii)
4
(iv)
(
−
2
)
Question
3
3.
A and B are two points on the x-axis and y-axis respectively.
If
(
(
−
5
)
,
3
)
is the mid-point of the join of A and B, find A and B
(i)
(
(
−
10
)
,
0
)
,
(
0
,
6
)
(ii)
(
(
−
9
)
,
(
−
1
)
)
,
(
0
,
6
)
(iii)
(
(
−
10
)
,
0
)
,
(
(
−
1
)
,
7
)
(iv)
(
(
−
8
)
,
2
)
,
(
0
,
6
)
(v)
(
(
−
12
)
,
(
−
2
)
)
,
(
0
,
6
)
Question
4
4.
The points
(
7
,
(
−
1
)
)
,
(
1
,
0
)
and
(
(
4
−
1
2
√
3
)
,
(
−
1
2
−
3
√
3
)
)
represent
(i)
equilateral triangle
(ii)
right angled triangle
(iii)
scalene triangle
(iv)
isosceles triangle
Question
5
5.
Find the ratio in which point
(
6
,
(
−
7
3
)
)
divides the join of points
(
6
,
0
)
and
(
6
,
(
−
3
)
)
(i)
8
:
2
(ii)
7
:
2
(iii)
6
:
2
(iv)
7
:
5
(v)
7
:
0
Question
6
6.
If point P
(
1
,
0
)
bisects A
(
6
,
(
−
7
)
)
and B
(
x
,
y
)
, find
(
x
,
y
)
(i)
(
(
−
5
)
,
8
)
(ii)
(
(
−
2
)
,
9
)
(iii)
(
(
−
3
)
,
6
)
(iv)
(
(
−
4
)
,
7
)
(v)
(
(
−
6
)
,
5
)
Question
7
7.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
2
,
(
−
1
)
)
and
(
(
−
7
)
,
(
−
3
)
)
(i)
(
−
3
x
−
4
y
+
4
)
=
0
(ii)
(
−
3
x
−
2
y
+
4
)
=
0
(iii)
(
18
x
+
4
y
+
53
)
=
0
(iv)
(
18
x
+
6
y
+
53
)
=
0
(v)
(
17
x
+
4
y
+
53
)
=
0
Question
8
8.
Distance of the given point from y-axis is
(i)
0
(ii)
3
Question
9
9.
Find the value of k such that the points
(
(
−
6
)
,
(
−
6
)
)
,
(
(
−
54
11
)
,
0
)
and
(k,5)
are collinear
(i)
-3
(ii)
-5
(iii)
-1
(iv)
-4
(v)
-7
Question
10
10.
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)
(
m
x
2
+
n
x
1
m + n
,
m
y
2
+
n
y
1
m + n
)
(iii)
(
n
x
2
+
m
x
1
m + n
,
n
y
2
+
m
y
1
m + n
)
(iv)
(
n
x
2
−
m
x
1
m - n
,
n
y
2
−
m
y
1
m - n
)
Question
11
11.
The points
(
(
−
1
)
,
4
)
,
(
1
,
(
−
4
)
)
and
(
(
−
1
4
)
,
1
)
represents
(i)
collinear points
(ii)
right angle triangle
(iii)
isoceles triangle
(iv)
equilateral triangle
Question
12
12.
If A
(
6
,
6
)
and B
(
7
,
(
−
7
)
)
are two points,
find the coordinates of the point C on AB produced so that AC = 2BC
(i)
(
6
,
(
−
22
)
)
(ii)
(
9
,
(
−
21
)
)
(iii)
(
7
,
(
−
19
)
)
(iv)
(
10
,
(
−
18
)
)
(v)
(
8
,
(
−
20
)
)
Question
13
13.
Find the coordinates of the mid points of the sides of the triangle formed by
(
1
,
(
−
3
)
)
,
(
(
−
5
)
,
4
)
and
(
(
−
4
)
,
5
)
(i)
(
(
−
2
)
,
1
2
)
,
(
(
−
5
2
)
,
13
2
)
,
(
(
−
3
2
)
,
1
)
(ii)
(
(
−
3
)
,
3
2
)
,
(
(
−
9
2
)
,
9
2
)
,
(
(
−
3
2
)
,
1
)
(iii)
(
(
−
2
)
,
1
2
)
,
(
(
−
9
2
)
,
9
2
)
,
(
(
−
1
2
)
,
0
)
(iv)
(
(
−
2
)
,
1
2
)
,
(
(
−
9
2
)
,
9
2
)
,
(
(
−
3
2
)
,
1
)
(v)
(
(
−
2
)
,
1
2
)
,
(
(
−
9
2
)
,
9
2
)
,
(
(
−
7
2
)
,
(
−
1
)
)
Question
14
14.
KM is the straight line of length
√
26
units.
If K has the coordinates
(
5
,
(
−
8
)
)
and M has coordinates
(k,-3)
,
find the possible values of k
(i)
(
6
,
4
)
(ii)
(
8
,
6
)
(iii)
(
5
,
5
)
(iv)
(
7
,
3
)
(v)
(
4
,
2
)
Question
15
15.
Find the point which is equidistant from the points
(
(
−
3
)
,
(
−
8
)
)
,
(
(
−
6
)
,
6
)
and
(
(
−
3
)
,
7
)
(i)
(
(
−
13
6
)
,
(
−
1
2
)
)
(ii)
(
(
−
7
6
)
,
(
−
3
2
)
)
(iii)
(
(
−
1
6
)
,
3
2
)
(iv)
(
(
−
25
6
)
,
(
−
5
2
)
)
(v)
(
(
−
19
6
)
,
1
2
)
Question
16
16.
The points
(
(
−
1
)
,
(
−
2
)
)
,
(
6
,
(
−
2
)
)
,
(
6
,
2
)
and
(
(
−
1
)
,
2
)
represents
(i)
square
(ii)
parallelogram
(iii)
rectangle
(iv)
rhombus
(v)
trapezium
Question
17
17.
Three vertices of a parallelogram are
(
(
−
1
)
,
(
−
6
)
)
,
(
6
,
(
−
6
)
)
and
(
10
,
(
−
1
)
)
.
Find the fourth vertex
(i)
(
1
,
(
−
3
)
)
(ii)
(
2
,
0
)
(iii)
(
5
,
1
)
(iv)
(
3
,
(
−
1
)
)
(v)
(
4
,
(
−
2
)
)
Question
18
18.
Find the coordinates of the orthocentre of the triangle
whose vertices are
(
(
−
5
)
,
(
−
5
)
)
,
(
5
,
(
−
4
)
)
and
(
(
−
5
)
,
1
)
(i)
(
(
−
5
2
)
,
(
−
2
)
)
(ii)
(
(
−
7
2
)
,
(
−
5
)
)
(iii)
(
(
−
11
2
)
,
(
−
3
)
)
(iv)
(
(
−
13
2
)
,
(
−
6
)
)
(v)
(
(
−
9
2
)
,
(
−
4
)
)
Question
19
19.
Find the radius of the circle passing through the points
(
(
−
1
)
,
7
)
,
(
(
−
4
)
,
3
)
and
(
(
−
6
)
,
(
−
4
)
)
(i)
5
26
√
7741
(ii)
5
26
√
7738
(iii)
19345
13
(iv)
5
26
√
7736
(v)
5
26
4
√
7738
Question
20
20.
Find the points on x-axis,
which are at a distance of
14
units
from the point
(
8
,
(
−
7
)
)
(i)
(
(
8
+
7
√
3
)
,
0
)
,
(
(
7
−
7
√
3
)
,
1
)
(ii)
(
(
6
+
7
√
3
)
,
(
−
2
)
)
,
(
(
8
−
7
√
3
)
,
0
)
(iii)
(
(
9
+
7
√
3
)
,
(
−
1
)
)
,
(
(
8
−
7
√
3
)
,
0
)
(iv)
(
(
10
+
7
√
3
)
,
2
)
,
(
(
8
−
7
√
3
)
,
0
)
(v)
(
(
8
+
7
√
3
)
,
0
)
,
(
(
8
−
7
√
3
)
,
0
)
Question
21
21.
Find the coordinates of the points of trisection of the line segment
joining the points
(
(
−
6
)
,
(
−
4
)
)
and
(
(
−
7
)
,
(
−
1
)
)
(i)
(
(
−
25
3
)
,
(
−
5
)
)
,
(
(
−
20
3
)
,
(
−
2
)
)
(ii)
(
(
−
13
3
)
,
(
−
1
)
)
,
(
(
−
20
3
)
,
(
−
2
)
)
(iii)
(
(
−
19
3
)
,
(
−
3
)
)
,
(
(
−
20
3
)
,
(
−
2
)
)
(iv)
(
(
−
16
3
)
,
(
−
4
)
)
,
(
(
−
20
3
)
,
(
−
2
)
)
(v)
(
(
−
19
3
)
,
(
−
3
)
)
,
(
(
−
23
3
)
,
(
−
1
)
)
Question
22
22.
Find the centre of the circle passing through
the points
(
2
,
(
−
1
)
)
,
(
5
,
5
)
and
(
2
,
(
−
8
)
)
(i)
(
37
2
,
(
−
5
2
)
)
(ii)
(
33
2
,
(
−
9
2
)
)
(iii)
(
29
2
,
(
−
13
2
)
)
(iv)
(
35
2
,
(
−
11
2
)
)
(v)
(
31
2
,
(
−
7
2
)
)
Question
23
23.
Find the coordinates of the circumcentre of the triangle
whose vertices are
(
0
,
6
)
,
(
1
,
(
−
2
)
)
and
(
(
−
5
)
,
5
)
(i)
(
(
−
143
82
)
,
141
82
)
(ii)
(
(
−
61
82
)
,
59
82
)
(iii)
(
(
−
307
82
)
,
(
−
23
82
)
)
(iv)
(
21
82
,
305
82
)
(v)
(
(
−
225
82
)
,
223
82
)
Question
24
24.
Distance of the point (8,9) from y-axis is
(i)
(
−
1
)
(ii)
9
(iii)
8
(iv)
1
(v)
17
Question
25
25.
The points
(
(
−
4
)
,
(
−
1
)
)
,
(
3
,
(
−
1
)
)
,
(
6
,
3
)
and
(
(
−
1
)
,
3
)
represent
(i)
square
(ii)
rectangle
(iii)
rhombus
(iv)
trapezium
(v)
parallelogram
Assignment Key
1) (v)
2) (ii)
3) (i)
4) (i)
5) (ii)
6) (iv)
7) (iii)
8) (ii)
9) (iv)
10) (ii)
11) (i)
12) (v)
13) (iv)
14) (i)
15) (i)
16) (iii)
17) (iv)
18) (v)
19) (ii)
20) (v)
21) (iii)
22) (ii)
23) (i)
24) (iii)
25) (v)
