EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Find the points on x-axis,
which are at a distance of
18
units
from the point
(
(
−
2
)
,
(
−
8
)
)
(i)
(
2
√
65
,
2
)
,
(
(
−
2
−
2
√
65
)
,
0
)
(ii)
(
(
−
2
+
2
√
65
)
,
0
)
,
(
(
−
2
−
2
√
65
)
,
0
)
(iii)
(
(
−
1
+
2
√
65
)
,
(
−
1
)
)
,
(
(
−
2
−
2
√
65
)
,
0
)
(iv)
(
(
−
4
+
2
√
65
)
,
(
−
2
)
)
,
(
(
−
2
−
2
√
65
)
,
0
)
(v)
(
(
−
2
+
2
√
65
)
,
0
)
,
(
(
−
3
−
2
√
65
)
,
1
)
Question
2
2.
Find the point which is equidistant from the points
(
0
,
(
−
2
)
)
,
(
(
−
1
)
,
0
)
and
(
5
,
(
−
5
)
)
(i)
(
97
14
,
17
14
)
(ii)
(
69
14
,
45
14
)
(iii)
(
55
14
,
3
14
)
(iv)
(
83
14
,
31
14
)
(v)
(
111
14
,
59
14
)
Question
3
3.
A point lies on negative side of y-axis at a distance of 6 units from x-axis. What are the coordinates of the point?
(i)
(
(
−
6
)
,
0
)
(ii)
(
0
,
(
−
6
)
)
(iii)
(
0
,
6
)
(iv)
(
6
,
0
)
Question
4
4.
A and B are two points on the x-axis and y-axis respectively.
If
(
(
−
6
)
,
7
)
is the mid-point of the join of A and B, find A and B
(i)
(
(
−
10
)
,
2
)
,
(
0
,
14
)
(ii)
(
(
−
14
)
,
(
−
2
)
)
,
(
0
,
14
)
(iii)
(
(
−
12
)
,
0
)
,
(
(
−
1
)
,
15
)
(iv)
(
(
−
11
)
,
(
−
1
)
)
,
(
0
,
14
)
(v)
(
(
−
12
)
,
0
)
,
(
0
,
14
)
Question
5
5.
Find the relation between x and y if the points
(
x
,
y
)
,
(
5
,
(
−
2
)
)
and
(
1
,
(
−
3
)
)
are collinear
(i)
(
−
3
x
−
2
y
−
3
)
=
0
(ii)
(
−
3
x
+
4
y
+
33
)
=
0
(iii)
(
−
x
−
2
y
+
1
)
=
0
(iv)
(
−
x
+
4
y
+
13
)
=
0
(v)
(
−
6
y
−
18
)
=
0
Question
6
6.
If point P
(
(
−
1
)
,
3
)
bisects A
(
(
−
3
)
,
5
)
and B
(
x
,
y
)
, find
(
x
,
y
)
(i)
(
0
,
2
)
(ii)
(
1
,
1
)
(iii)
(
3
,
3
)
(iv)
(
2
,
0
)
(v)
(
(
−
1
)
,
(
−
1
)
)
Question
7
7.
Find the distance of the point
(
3
,
(
−
3
)
)
from origin
(i)
3
√
-1
(ii)
3
4
√
2
(iii)
3
√
4
(iv)
3
√
2
(v)
6
Question
8
8.
The points
(
(
−
8
)
,
0
)
,
(
(
−
4
)
,
4
)
and
(
(
−
6
−
2
√
3
)
,
(
2
+
2
√
3
)
)
represent
(i)
isosceles triangle
(ii)
equilateral triangle
(iii)
right angled triangle
(iv)
scalene triangle
Question
9
9.
The mid-point of the join of the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is
(i)
(
x
1
+
x
2
3
,
y
1
+
y
2
3
)
(ii)
(
x
1
−
x
2
2
,
y
1
−
y
2
2
)
(iii)
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(iv)
(
y
1
−
y
2
2
,
x
1
−
x
2
2
)
(v)
(
x
1
−
x
2
3
,
y
1
−
y
2
3
)
Question
10
10.
The mid-point of the join of points
(
2
,
1
)
and
(
(
−
5
)
,
(
−
6
)
)
is
(i)
(
1
2
,
(
−
1
2
)
)
(ii)
(
(
−
3
2
)
,
(
−
5
2
)
)
(iii)
(
(
−
1
2
)
,
(
−
7
2
)
)
(iv)
(
(
−
7
2
)
,
(
−
9
2
)
)
(v)
(
(
−
5
2
)
,
(
−
3
2
)
)
Question
11
11.
Find the points on y-axis,
which are at a distance of
13
units
from the point
(
7
,
1
)
(i)
(
0
,
(
1
+
2
√
30
)
)
,
(
0
,
(
1
−
2
√
30
)
)
(ii)
(
(
−
2
)
,
(
−
1
+
2
√
30
)
)
,
(
0
,
(
1
−
2
√
30
)
)
(iii)
(
2
,
(
3
+
2
√
30
)
)
,
(
0
,
(
1
−
2
√
30
)
)
(iv)
(
1
,
2
√
30
)
,
(
0
,
(
1
−
2
√
30
)
)
(v)
(
0
,
(
1
+
2
√
30
)
)
,
(
(
−
1
)
,
(
2
−
2
√
30
)
)
Question
12
12.
If point P
(x,2)
is equidistant from the points
(
5
,
3
)
and
(
6
,
2
)
, find x
(i)
8
(ii)
6
(iii)
5
(iv)
4
(v)
3
Question
13
13.
The line
(
2
x
+
2
y
+
8
)
=
0
bisects which of the following pairs of points?
(i)
(
(
−
8
)
,
2
)
,
(
(
−
7
)
,
5
)
(ii)
(
(
−
6
)
,
4
)
(iii)
(
(
−
7
)
,
1
)
,
(
(
−
6
)
,
4
)
(iv)
(
(
−
10
)
,
0
)
,
(
(
−
6
)
,
4
)
(v)
(
(
−
8
)
,
2
)
,
(
(
−
6
)
,
4
)
Question
14
14.
Find the value of k such that the points
(
(
−
7
)
,
(
−
1
)
)
,
(
(
−
19
13
)
,
23
13
)
and
(5,k)
are collinear
(i)
3
(ii)
8
(iii)
4
(iv)
6
(v)
5
Question
15
15.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
4
,
3
2
)
,
(
5
2
,
1
2
)
and
(
1
2
,
5
)
(i)
(
2
,
6
)
,
(
6
,
(
−
3
)
)
,
(
0
,
3
)
(ii)
(
2
,
6
)
,
(
6
,
(
−
3
)
)
,
(
(
−
1
)
,
4
)
(iii)
(
1
,
7
)
,
(
6
,
(
−
3
)
)
,
(
(
−
1
)
,
4
)
(iv)
(
2
,
6
)
,
(
8
,
(
−
1
)
)
,
(
(
−
1
)
,
4
)
(v)
(
2
,
6
)
,
(
6
,
(
−
3
)
)
,
(
(
−
3
)
,
2
)
Question
16
16.
Find the point on y-axis which is equidistant
from the points
(
(
−
5
)
,
(
−
8
)
)
and
(
(
−
6
)
,
(
−
5
)
)
(i)
(
1
,
(
−
17
3
)
)
(ii)
(
(
−
2
)
,
(
−
20
3
)
)
(iii)
(
(
−
1
)
,
(
−
11
3
)
)
(iv)
(
0
,
(
−
14
3
)
)
(v)
(
2
,
(
−
8
3
)
)
Question
17
17.
The points
(
(
−
7
)
,
(
−
8
)
)
,
(
7
,
8
)
and
(
(
−
7
3
)
,
(
−
8
3
)
)
represents
(i)
equilateral triangle
(ii)
right angle triangle
(iii)
collinear points
(iv)
isoceles triangle
Question
18
18.
Find the lengths of the medians of a triangle whose vertices are
(
8
,
(
−
7
)
)
,
(
(
−
7
)
,
(
−
4
)
)
and
(
(
−
5
)
,
6
)
(i)
2
√
65
,
13
2
√
2
,
5
2
√
26
(ii)
3
2
√
26
,
√
26
,
√
26
(iii)
√
26
,
13
2
√
2
,
3
2
√
26
Question
19
19.
Find the centre of the circle, the endpoints of whose
diameter are
(
(
−
8
)
,
(
−
1
)
)
and
(
(
−
3
)
,
(
−
8
)
)
(i)
(
(
−
11
2
)
,
9
2
)
(ii)
(
(
−
11
2
)
,
(
−
9
2
)
)
(iii)
(
(
−
9
2
)
,
(
−
11
2
)
)
(iv)
(
11
2
,
(
−
9
2
)
)
(v)
(
11
2
,
9
2
)
Question
20
20.
A point lies on negative side of x-axis at a distance of 1 units from y-axis. What are the coordinates of the point?
(i)
(
(
−
1
)
,
0
)
(ii)
(
1
,
0
)
(iii)
(
0
,
1
)
(iv)
(
0
,
(
−
1
)
)
Question
21
21.
Find the ratio in which point
(
(
−
11
5
)
,
(
−
58
15
)
)
divides the join of points
(
(
−
7
)
,
(
−
6
)
)
and
(
2
,
(
−
2
)
)
(i)
8
:
7
(ii)
8
:
5
(iii)
7
:
7
(iv)
9
:
7
(v)
8
:
10
Question
22
22.
The points
(
(
−
6
)
,
(
−
3
)
)
,
(
(
−
3
)
,
1
)
and
(
1
,
(
−
2
)
)
represent
(i)
scalene triangle
(ii)
equilateral triangle
(iii)
right angle triangle
(iv)
isosceles right angled triangle
(v)
collinear points
Question
23
23.
The points
(
6
,
8
)
,
(
6
,
(
−
2
)
)
and
(
(
−
8
)
,
1
)
represent
(i)
right angle triangle
(ii)
equilateral triangle
(iii)
isosceles triangle
(iv)
scalene triangle
(v)
collinear points
Question
24
24.
Find the point that bisects
(
(
−
8
)
,
6
)
and
(
(
−
8
)
,
(
−
1
)
)
(i)
(
(
−
6
)
,
9
2
)
(ii)
(
(
−
10
)
,
1
2
)
(iii)
(
(
−
9
)
,
7
2
)
(iv)
(
(
−
7
)
,
3
2
)
(v)
(
(
−
8
)
,
5
2
)
Question
25
25.
Determine the ratio in which the line
(
−
9
y
+
18
)
=
0
divides the join of points
(
1
,
(
−
5
)
)
and
(
0
,
4
)
(i)
7
:
2
(ii)
8
:
2
(iii)
6
:
2
(iv)
7
:
0
(v)
7
:
5
Assignment Key
1) (ii)
2) (iv)
3) (ii)
4) (v)
5) (iv)
6) (ii)
7) (iv)
8) (ii)
9) (iii)
10) (ii)
11) (i)
12) (iii)
13) (v)
14) (v)
15) (ii)
16) (iv)
17) (iii)
18) (i)
19) (ii)
20) (i)
21) (i)
22) (iv)
23) (iv)
24) (v)
25) (i)
