EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
(
−
4
)
,
(
−
4
)
)
and
(
2
,
5
)
(i)
(
3
x
+
6
y
+
1
)
=
0
(ii)
(
12
x
+
48
)
=
0
(iii)
(
4
x
+
8
y
+
1
)
=
0
(iv)
(
12
x
+
46
)
=
0
(v)
(
4
x
+
6
y
+
1
)
=
0
Question
2
2.
Find the value of k such that the points
(
(
−
5
)
,
0
)
,
(
13
4
,
3
)
and
(k,4)
are collinear
(i)
8
(ii)
5
(iii)
3
(iv)
6
(v)
7
Question
3
3.
Distance of the given point from y-axis is
(i)
1
(ii)
-1
(iii)
3
(iv)
2
Question
4
4.
Find the area of the triangle
formed by the points
(
(
−
5
)
,
5
)
,
(
(
−
6
)
,
(
−
1
)
)
and
(
(
−
2
)
,
(
−
2
)
)
(i)
23
2
(ii)
49
4
(iii)
27
2
(iv)
25
2
(v)
13
Question
5
5.
Find the area of the quadrilateral formed by
(
(
−
3
)
,
(
−
2
)
)
,
(
3
,
4
)
,
(
(
−
2
)
,
6
)
and
(
(
−
5
)
,
6
)
(i)
32
(ii)
30
(iii)
35
(iv)
33
(v)
34
Question
6
6.
Determine the ratio in which the line
(
x
−
12
y
+
53
)
=
0
divides the join of points
(
6
,
(
−
2
)
)
and
(
1
,
9
)
(i)
83
:
57
(ii)
82
:
54
(iii)
83
:
54
(iv)
84
:
54
(v)
83
:
52
Question
7
7.
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)
(
0
,
3
)
(iii)
(
3
,
0
)
(iv)
(
(
−
3
)
,
0
)
Question
8
8.
The points
(
(
−
3
)
,
(
−
8
)
)
,
(
6
,
(
−
5
)
)
and
(
(
−
2
)
,
4
)
represent
(i)
isosceles triangle
(ii)
scalene triangle
(iii)
collinear points
(iv)
equilateral triangle
(v)
right angle triangle
Question
9
9.
Find the lengths of the medians of a triangle whose vertices are
(
(
−
4
)
,
4
)
,
(
(
−
8
)
,
(
−
7
)
)
and
(
(
−
2
)
,
(
−
5
)
)
(i)
√
10
,
1
2
√
85
,
1
2
√
137
(ii)
√
101
,
1
2
√
269
,
1
2
√
113
(iii)
1
2
√
137
,
√
10
,
√
10
Question
10
10.
The mid-point of the join of points
(
2
,
0
)
and
(
(
−
2
)
,
(
−
5
)
)
is
(i)
(
1
,
(
−
7
2
)
)
(ii)
(
(
−
2
)
,
(
−
9
2
)
)
(iii)
(
(
−
1
)
,
(
−
3
2
)
)
(iv)
(
0
,
(
−
5
2
)
)
(v)
(
2
,
(
−
1
2
)
)
Question
11
11.
Find the circumradius of the triangle whose vertices are
(
(
−
2
)
,
0
)
,
(
5
,
4
)
and
(
2
,
(
−
3
)
)
(i)
5
74
4
√
3770
(ii)
5
74
√
3773
(iii)
9425
37
(iv)
5
74
√
3767
(v)
5
74
√
3770
Question
12
12.
Find the coordinates of the points of trisection of the line segment
joining the points
(
8
,
(
−
2
)
)
and
(
(
−
4
)
,
4
)
(i)
(
4
,
0
)
,
(
0
,
2
)
(ii)
(
6
,
2
)
,
(
0
,
2
)
(iii)
(
5
,
(
−
1
)
)
,
(
0
,
2
)
(iv)
(
2
,
(
−
2
)
)
,
(
0
,
2
)
(v)
(
4
,
0
)
,
(
(
−
1
)
,
3
)
Question
13
13.
The points
(
(
−
3
)
,
(
−
1
)
)
,
(
1
,
3
)
,
(
5
,
(
−
1
)
)
and
(
1
,
(
−
5
)
)
represent
(i)
parallelogram
(ii)
rectangle
(iii)
trapezium
(iv)
square
(v)
rhombus
Question
14
14.
The points
(
6
,
3
)
,
(
(
−
6
)
,
6
)
and
(
4
,
0
)
represent
(i)
scalene triangle
(ii)
equilateral triangle
(iii)
isosceles triangle
(iv)
right angle triangle
(v)
collinear points
Question
15
15.
Find the centre of the circle passing through
the points
(
0
,
5
)
,
(
(
−
1
)
,
(
−
2
)
)
and
(
8
,
6
)
(i)
(
145
22
,
61
22
)
(ii)
(
79
22
,
39
22
)
(iii)
(
123
22
,
(
−
5
22
)
)
(iv)
(
57
22
,
(
−
27
22
)
)
(v)
(
101
22
,
17
22
)
Question
16
16.
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)
(
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)
(
m
x
2
+
n
x
1
m + n
,
m
y
2
+
n
y
1
m + n
)
Question
17
17.
If point P
(x,2)
is equidistant from the points
(
(
−
3
)
,
5
)
and
(
(
−
8
)
,
7
)
, find x
(i)
(
-71
10
)
(ii)
(
-69
10
)
(iii)
(
-85
12
)
(iv)
(
-73
10
)
(v)
(
-57
8
)
Question
18
18.
The points
(
(
−
2
)
,
(
−
1
)
)
,
(
5
,
(
−
1
)
)
and
(
5
,
2
)
represent
(i)
right angle triangle
(ii)
scalene triangle
(iii)
isosceles right angled triangle
(iv)
equilateral triangle
(v)
collinear points
Question
19
19.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
1
,
6
)
,
(
1
,
5
2
)
and
(
(
−
2
)
,
9
2
)
(i)
(
(
−
2
)
,
8
)
,
(
6
,
6
)
,
(
(
−
2
)
,
1
)
(ii)
(
(
−
2
)
,
8
)
,
(
4
,
4
)
,
(
(
−
4
)
,
(
−
1
)
)
(iii)
(
(
−
3
)
,
9
)
,
(
4
,
4
)
,
(
(
−
2
)
,
1
)
(iv)
(
(
−
2
)
,
8
)
,
(
4
,
4
)
,
(
(
−
2
)
,
1
)
(v)
(
(
−
2
)
,
8
)
,
(
4
,
4
)
,
(
(
−
1
)
,
0
)
Question
20
20.
Find the distance of the point
(
8
,
5
)
from origin
(i)
89
(ii)
√
92
(iii)
√
89
(iv)
√
86
(v)
4
√
89
Question
21
21.
The points
(
(
−
1
)
,
(
−
6
)
)
,
(
7
,
(
−
6
)
)
,
(
7
,
(
−
3
)
)
and
(
(
−
1
)
,
(
−
3
)
)
represents
(i)
rectangle
(ii)
parallelogram
(iii)
square
(iv)
trapezium
(v)
rhombus
Question
22
22.
The centre of a circle is
(
3
2
,
1
)
.
Find the other end of the diameter whose one end point is
(
4
,
6
)
(i)
(
(
−
4
)
,
(
−
1
)
)
(ii)
(
(
−
1
)
,
(
−
4
)
)
(iii)
(
1
,
(
−
4
)
)
(iv)
(
(
−
1
)
,
4
)
(v)
(
1
,
4
)
Question
23
23.
Distance of the point (3,4) from x-axis is
(i)
4
(ii)
1
(iii)
(
−
1
)
(iv)
7
(v)
3
Question
24
24.
Find the centre of the circle, the endpoints of whose
diameter are
(
(
−
2
)
,
(
−
1
)
)
and
(
(
−
1
)
,
5
)
(i)
(
3
2
,
(
−
2
)
)
(ii)
(
(
−
3
2
)
,
2
)
(iii)
(
3
2
,
2
)
(iv)
(
(
−
3
2
)
,
(
−
2
)
)
(v)
(
2
,
(
−
3
2
)
)
Question
25
25.
The points
(
2
,
(
−
6
)
)
,
(
(
−
2
)
,
6
)
and
(
2
13
,
(
−
6
13
)
)
represents
(i)
right angle triangle
(ii)
equilateral triangle
(iii)
isoceles triangle
(iv)
collinear points
Assignment Key
1) (v)
2) (iv)
3) (i)
4) (iv)
5) (iv)
6) (iii)
7) (iii)
8) (i)
9) (ii)
10) (iv)
11) (v)
12) (i)
13) (iv)
14) (i)
15) (v)
16) (iv)
17) (i)
18) (i)
19) (iv)
20) (iii)
21) (i)
22) (ii)
23) (i)
24) (ii)
25) (iv)
