EduSahara™ Assignment
Name : Distance Formula
Chapter : Coordinate Geometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Find the distance between the points
(
1
,
(
−
4
)
)
and
(
4
,
0
)
(i)
6
(ii)
4
(iii)
2
(iv)
8
(v)
5
Question
2
2.
Find the perimeter of the triangle formed by the points
(
5
,
3
)
,
(
(
−
2
)
,
(
−
8
)
)
and
(
(
−
8
)
,
8
)
(i)
(
√
170
+
2
√
73
+
4
√
194
)
(ii)
(
√
170
+
2
√
71
+
√
194
)
(iii)
(
√
170
+
2
√
73
+
194
)
(iv)
(
√
170
+
2
√
75
+
√
194
)
(v)
(
√
170
+
2
√
73
+
√
194
)
Question
3
3.
Find the lengths of the sides of the triangle formed by the points
(
5
,
(
−
3
)
)
,
(
0
,
1
)
and
(
6
,
(
−
1
)
)
(i)
√
41
,
2
√
10
,
√
5
(ii)
√
41
,
2
√
10
,
√
8
(iii)
√
41
,
20
,
√
5
(iv)
4
√
41
,
2
√
10
,
√
5
Question
4
4.
Distance of the point (4,8) from x-axis is
(i)
4
(ii)
8
(iii)
(
−
4
)
(iv)
12
Question
5
5.
Distance of the point (1,3) from y-axis is
(i)
3
(ii)
(
−
2
)
(iii)
4
(iv)
2
(v)
1
Question
6
6.
Distance of the given point from x-axis is
(i)
5
(ii)
13
(iii)
40
(iv)
8
(v)
3
Question
7
7.
Distance of the given point from y-axis is
(i)
5
(ii)
-3
(iii)
10
(iv)
2
(v)
7
Question
8
8.
Find the distance of the point
(
(
−
2
)
,
7
)
from origin
(i)
53
(ii)
√
53
(iii)
4
√
53
(iv)
√
56
(v)
√
51
Question
9
9.
A is a point on x-axis with abscissa
0
and B is a point on y-axis
with ordinate
8
.
Find the distance between A and B
(i)
7
(ii)
8
(iii)
9
(iv)
5
(v)
11
Question
10
10.
KM is the straight line of length
3
√
5
units.
If K has the coordinates
(
5
,
3
)
and M has coordinates
(k,6)
,
find the possible values of k
(i)
(
13
,
1
)
(ii)
(
11
,
(
−
1
)
)
(iii)
(
12
,
(
−
2
)
)
(iv)
(
10
,
0
)
(v)
(
9
,
(
−
3
)
)
Question
11
11.
Find the point on x-axis which is equidistant
from the points
(
3
,
(
−
3
)
)
and
(
2
,
(
−
8
)
)
(i)
(
(
−
27
)
,
(
−
2
)
)
(ii)
(
(
−
25
)
,
0
)
(iii)
(
(
−
26
)
,
1
)
(iv)
(
(
−
23
)
,
2
)
(v)
(
(
−
24
)
,
(
−
1
)
)
Question
12
12.
Find the point on y-axis which is equidistant
from the points
(
(
−
4
)
,
(
−
2
)
)
and
(
(
−
7
)
,
8
)
(i)
(
2
,
133
20
)
(ii)
(
(
−
1
)
,
113
20
)
(iii)
(
0
,
93
20
)
(iv)
(
(
−
2
)
,
53
20
)
(v)
(
1
,
73
20
)
Question
13
13.
Find the points on x-axis,
which are at a distance of
10
units
from the point
(
3
,
(
−
3
)
)
(i)
(
(
3
+
√
91
)
,
0
)
,
(
(
3
−
√
91
)
,
0
)
(ii)
(
(
1
+
√
91
)
,
(
−
2
)
)
,
(
(
3
−
√
91
)
,
0
)
(iii)
(
(
5
+
√
91
)
,
2
)
,
(
(
3
−
√
91
)
,
0
)
(iv)
(
(
4
+
√
91
)
,
(
−
1
)
)
,
(
(
3
−
√
91
)
,
0
)
(v)
(
(
3
+
√
91
)
,
0
)
,
(
(
2
−
√
91
)
,
1
)
Question
14
14.
Find the points on y-axis,
which are at a distance of
11
units
from the point
(
6
,
(
−
6
)
)
(i)
(
2
,
(
−
4
+
√
85
)
)
,
(
0
,
(
−
6
−
√
85
)
)
(ii)
(
(
−
2
)
,
(
−
8
+
√
85
)
)
,
(
0
,
(
−
6
−
√
85
)
)
(iii)
(
1
,
(
−
7
+
√
85
)
)
,
(
0
,
(
−
6
−
√
85
)
)
(iv)
(
0
,
(
−
6
+
√
85
)
)
,
(
0
,
(
−
6
−
√
85
)
)
(v)
(
0
,
(
−
6
+
√
85
)
)
,
(
(
−
1
)
,
(
−
5
−
√
85
)
)
Question
15
15.
Find the lengths of the medians of a triangle whose vertices are
(
1
,
1
)
,
(
(
−
8
)
,
3
)
and
(
(
−
4
)
,
1
)
(i)
√
5
,
5
2
,
1
2
√
85
(ii)
5
√
2
,
1
2
√
185
,
1
2
√
5
(iii)
1
2
√
85
,
√
5
,
√
5
Question
16
16.
If point P
(x,4)
is equidistant from the points
(
0
,
(
−
5
)
)
and
(
3
,
5
)
, find x
(i)
(
-49
4
)
(ii)
(
-93
8
)
(iii)
(
-71
6
)
(iv)
(
-73
6
)
(v)
(
-23
2
)
Question
17
17.
If point P
(
(
−
23
24
)
,
4
)
is equidistant from the points
(a,4)
and
(
5
,
5
)
, find a
(i)
-6
(ii)
-4
(iii)
-7
(iv)
-8
(v)
-9
Question
18
18.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
7
,
(
−
1
)
)
and
(
(
−
8
)
,
1
)
(i)
(
2
x
+
10
y
−
1
)
=
0
(ii)
(
−
30
x
+
4
y
−
15
)
=
0
(iii)
(
2
x
+
13
y
−
1
)
=
0
(iv)
(
−
31
x
+
4
y
−
15
)
=
0
(v)
(
−
30
x
+
6
y
−
15
)
=
0
Assignment Key
1) (v)
2) (v)
3) (i)
4) (ii)
5) (v)
6) (iv)
7) (iv)
8) (ii)
9) (ii)
10) (ii)
11) (ii)
12) (iii)
13) (i)
14) (iv)
15) (ii)
16) (iii)
17) (iii)
18) (ii)
