EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
If the point
(
(
−
12
11
)
,
59
11
)
divides the join of points
(
3
,
(
−
2
)
)
and
(
x
,
y
)
in the ratio
9
:
2
, find
(
x
,
y
)
(i)
(
(
−
4
)
,
5
)
(ii)
(
(
−
3
)
,
8
)
(iii)
(
0
,
9
)
(iv)
(
(
−
1
)
,
6
)
(v)
(
(
−
2
)
,
7
)
Question
2
2.
The points
(
(
−
2
)
,
(
−
6
)
)
,
(
4
,
(
−
11
)
)
,
(
10
,
(
−
6
)
)
and
(
4
,
(
−
1
)
)
represent
(i)
square
(ii)
parallelogram
(iii)
rhombus
(iv)
trapezium
(v)
rectangle
Question
3
3.
The points
(
(
−
3
)
,
(
−
5
)
)
,
(
8
,
(
−
8
)
)
and
(
6
,
(
−
6
)
)
represent
(i)
collinear points
(ii)
scalene triangle
(iii)
equilateral triangle
(iv)
right angle triangle
(v)
isosceles triangle
Question
4
4.
Find the ratio in which point
(
(
−
18
5
)
,
6
5
)
divides the join of points
(
2
,
6
)
and
(
(
−
5
)
,
0
)
(i)
9
:
2
(ii)
8
:
5
(iii)
8
:
2
(iv)
8
:
0
(v)
7
:
2
Question
5
5.
Find the relation between x and y if the points
(
x
,
y
)
,
(
(
−
5
)
,
2
)
and
(
8
,
1
)
are collinear
(i)
(
x
+
16
y
−
24
)
=
0
(ii)
(
4
x
−
16
y
+
64
)
=
0
(iii)
(
3
y
−
6
)
=
0
(iv)
(
−
x
−
13
y
+
21
)
=
0
(v)
(
5
x
−
40
)
=
0
Question
6
6.
A point lies on positive side of y-axis at a distance of 5 units from x-axis. What are the coordinates of the point?
(i)
(
0
,
(
−
5
)
)
(ii)
(
(
−
5
)
,
0
)
(iii)
(
5
,
0
)
(iv)
(
0
,
5
)
Question
7
7.
The coordinates of the origin are
(i)
(
5
,
0
)
(ii)
(
0
,
0
)
(iii)
(
1
,
1
)
(iv)
(
0
,
8
)
(v)
(
1
,
0
)
Question
8
8.
The points
(
3
,
6
)
,
(
(
−
3
)
,
(
−
6
)
)
and
(
21
13
,
42
13
)
represents
(i)
right angle triangle
(ii)
equilateral triangle
(iii)
collinear points
(iv)
isoceles triangle
Question
9
9.
Three vertices of a parallelogram are
(
(
−
3
)
,
(
−
6
)
)
,
(
3
,
(
−
6
)
)
and
(
6
,
(
−
1
)
)
.
Find the fourth vertex
(i)
(
1
,
(
−
2
)
)
(ii)
(
(
−
1
)
,
0
)
(iii)
(
(
−
2
)
,
(
−
3
)
)
(iv)
(
0
,
(
−
1
)
)
(v)
(
2
,
1
)
Question
10
10.
If point P
(x,6)
is equidistant from the points
(
(
−
2
)
,
(
−
4
)
)
and
(
0
,
5
)
, find x
(i)
(
-105
4
)
(ii)
(
-103
4
)
(iii)
(
-51
2
)
(iv)
(
-101
4
)
(v)
(
-53
2
)
Question
11
11.
Find the coordinates of the points of trisection of the line segment
joining the points
(
5
,
1
)
and
(
8
,
(
−
6
)
)
(i)
(
7
,
(
−
7
3
)
)
,
(
7
,
(
−
11
3
)
)
(ii)
(
8
,
2
3
)
,
(
7
,
(
−
11
3
)
)
(iii)
(
6
,
(
−
4
3
)
)
,
(
6
,
(
−
8
3
)
)
(iv)
(
6
,
(
−
4
3
)
)
,
(
7
,
(
−
11
3
)
)
(v)
(
4
,
(
−
10
3
)
)
,
(
7
,
(
−
11
3
)
)
Question
12
12.
The points
(
(
−
6
)
,
(
−
6
)
)
,
(
(
−
2
)
,
(
−
3
)
)
and
(
1
,
(
−
7
)
)
represent
(i)
equilateral triangle
(ii)
isosceles right angled triangle
(iii)
collinear points
(iv)
right angle triangle
(v)
scalene triangle
Question
13
13.
KM is the straight line of length
2
√
58
units.
If K has the coordinates
(
(
−
6
)
,
0
)
and M has coordinates
(k,-6)
,
find the possible values of k
(i)
(
6
,
(
−
22
)
)
(ii)
(
9
,
(
−
21
)
)
(iii)
(
7
,
(
−
19
)
)
(iv)
(
8
,
(
−
20
)
)
(v)
(
10
,
(
−
18
)
)
Question
14
14.
Distance of the point (7,6) from y-axis is
(i)
(
−
1
)
(ii)
13
(iii)
7
(iv)
6
(v)
1
Question
15
15.
Find the lengths of the sides of the triangle formed by the points
(
4
,
2
)
,
(
5
,
(
−
5
)
)
and
(
7
,
3
)
(i)
5
4
√
2
,
2
√
17
,
√
10
(ii)
5
√
2
,
34
,
√
10
(iii)
5
√
2
,
2
√
17
,
√
12
(iv)
5
√
2
,
2
√
17
,
√
10
Question
16
16.
Find the point which is equidistant from the points
(
(
−
3
)
,
7
)
,
(
(
−
1
)
,
5
)
and
(
8
,
3
)
(i)
(
79
14
,
191
14
)
(ii)
(
107
14
,
219
14
)
(iii)
(
93
14
,
177
14
)
(iv)
(
65
14
,
205
14
)
(v)
(
51
14
,
163
14
)
Question
17
17.
Find the area of the triangle
formed by the points
(
5
,
(
−
2
)
)
,
(
5
,
(
−
7
)
)
and
(
(
−
3
)
,
(
−
2
)
)
(i)
20
(ii)
22
(iii)
18
(iv)
19
(v)
21
Question
18
18.
A point lies on negative side of y-axis at a distance of 1 units from x-axis. What are the coordinates of the point?
(i)
(
1
,
0
)
(ii)
(
0
,
1
)
(iii)
(
(
−
1
)
,
0
)
(iv)
(
0
,
(
−
1
)
)
Question
19
19.
A point lies on negative side of x-axis at a distance of 5 units from y-axis. What are the coordinates of the point?
(i)
(
5
,
0
)
(ii)
(
0
,
(
−
5
)
)
(iii)
(
0
,
5
)
(iv)
(
(
−
5
)
,
0
)
Question
20
20.
Find the point that bisects
(
1
,
(
−
3
)
)
and
(
6
,
(
−
1
)
)
(i)
(
9
2
,
(
−
3
)
)
(ii)
(
7
2
,
(
−
2
)
)
(iii)
(
5
2
,
(
−
1
)
)
(iv)
(
3
2
,
(
−
4
)
)
(v)
(
11
2
,
0
)
Question
21
21.
In what ratio is the join of
(
4
,
(
−
9
)
)
and
(
8
,
6
)
divided by the line
(
−
y
−
7
)
=
0
?
(i)
2
:
16
(ii)
2
:
13
(iii)
1
:
13
(iv)
3
:
13
(v)
2
:
11
Question
22
22.
The points
(
(
−
1
)
,
(
−
4
)
)
,
(
5
,
(
−
4
)
)
,
(
5
,
0
)
and
(
(
−
1
)
,
0
)
represents
(i)
rectangle
(ii)
rhombus
(iii)
square
(iv)
parallelogram
(v)
trapezium
Question
23
23.
The line
(
−
x
+
5
y
+
13
)
=
0
bisects which of the following pairs of points?
(i)
(
3
,
(
−
1
)
)
,
(
6
,
(
−
4
)
)
(ii)
(
6
,
0
)
,
(
6
,
(
−
4
)
)
(iii)
(
5
,
1
)
,
(
5
,
(
−
3
)
)
(iv)
(
7
,
3
)
,
(
6
,
(
−
4
)
)
(v)
(
5
,
1
)
,
(
6
,
(
−
4
)
)
Question
24
24.
Find the distance between the points
(
(
−
7
)
,
0
)
and
(
5
,
6
)
(i)
6
√
2
(ii)
6
√
8
(iii)
6
√
5
(iv)
6
4
√
5
(v)
30
Question
25
25.
Find the centre of the circle passing through
the points
(
5
,
6
)
,
(
(
−
3
)
,
(
−
1
)
)
and
(
(
−
6
)
,
0
)
(i)
(
(
−
15
58
)
,
477
58
)
(ii)
(
(
−
247
58
)
,
245
58
)
(iii)
(
(
−
131
58
)
,
361
58
)
(iv)
(
(
−
189
58
)
,
419
58
)
(v)
(
(
−
73
58
)
,
303
58
)
Assignment Key
1) (v)
2) (iii)
3) (ii)
4) (iii)
5) (iv)
6) (iv)
7) (ii)
8) (iii)
9) (iv)
10) (ii)
11) (iv)
12) (ii)
13) (iv)
14) (iii)
15) (iv)
16) (i)
17) (i)
18) (iv)
19) (iv)
20) (ii)
21) (ii)
22) (i)
23) (v)
24) (iii)
25) (iii)
