EduSahara™ Assignment
Name : Distance between Two Points
Chapter : Coordinate Geometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Which of the following is a point on the positive x-axis?
(i)
(
(
−
7
)
,
0
)
(ii)
(
(
−
1
)
,
6
)
(iii)
(
4
,
0
)
(iv)
(
0
,
4
)
(v)
(
0
,
(
−
8
)
)
Question
2
2.
Which of the following is a point on the negative x-axis?
(i)
(
8
,
0
)
(ii)
(
(
−
2
)
,
9
)
(iii)
(
0
,
3
)
(iv)
(
(
−
7
)
,
0
)
(v)
(
0
,
(
−
2
)
)
Question
3
3.
Which of the following is a point on the positive y-axis?
(i)
(
(
−
6
)
,
5
)
(ii)
(
9
,
0
)
(iii)
(
(
−
8
)
,
0
)
(iv)
(
0
,
8
)
(v)
(
0
,
(
−
4
)
)
Question
4
4.
Which of the following is a point on the negative y-axis?
(i)
(
0
,
9
)
(ii)
(
0
,
(
−
3
)
)
(iii)
(
(
−
8
)
,
1
)
(iv)
(
1
,
0
)
(v)
(
(
−
2
)
,
0
)
Question
5
5.
Which of the following is a point on the x-axis?
(i)
(
(
−
3
)
,
4
)
(ii)
(
9
,
1
)
(iii)
(
0
,
5
)
(iv)
(
3
,
0
)
(v)
(
5
,
(
−
4
)
)
Question
6
6.
Which of the following is a point on the y-axis?
(i)
(
(
−
8
)
,
4
)
(ii)
(
3
,
(
−
7
)
)
(iii)
(
7
,
8
)
(iv)
(
0
,
5
)
(v)
(
3
,
0
)
Question
7
7.
The coordinates of a point which is 6 units away from x-axis and 2 units away from y-axis in the first quadrant is
(i)
(
2
,
(
−
6
)
)
(ii)
(
2
,
6
)
(iii)
(
6
,
2
)
(iv)
(
(
−
2
)
,
6
)
(v)
(
(
−
2
)
,
(
−
6
)
)
Question
8
8.
The coordinates of a point which is 6 units away from x-axis and 8 units away from y-axis in the second quadrant is
(i)
(
6
,
(
−
8
)
)
(ii)
(
8
,
(
−
6
)
)
(iii)
(
(
−
8
)
,
6
)
(iv)
(
(
−
8
)
,
(
−
6
)
)
(v)
(
8
,
6
)
Question
9
9.
The coordinates of a point which is 3 units away from x-axis and 4 units away from y-axis in the third quadrant is
(i)
(
4
,
(
−
3
)
)
(ii)
(
(
−
3
)
,
(
−
4
)
)
(iii)
(
4
,
3
)
(iv)
(
(
−
4
)
,
(
−
3
)
)
(v)
(
(
−
4
)
,
3
)
Question
10
10.
The coordinates of a point which is 4 units away from x-axis and 4 units away from y-axis in the fourth quadrant is
(i)
(
(
−
4
)
,
(
−
4
)
)
(ii)
(
4
,
4
)
(iii)
(
(
−
4
)
,
4
)
(iv)
(
4
,
(
−
4
)
)
Question
11
11.
Find the distance between the points
(
(
−
3
)
,
(
−
3
)
)
and
(
(
−
4
)
,
(
−
2
)
)
(i)
4
√
2
(ii)
√
-1
(iii)
2
(iv)
√
2
(v)
√
5
Question
12
12.
Find the perimeter of the triangle formed by the points
(
(
−
3
)
,
(
−
7
)
)
,
(
(
−
6
)
,
(
−
2
)
)
and
(
4
,
1
)
(i)
(
√
34
+
√
111
+
√
113
)
(ii)
(
√
34
+
√
109
+
√
113
)
(iii)
(
√
34
+
√
109
+
4
√
113
)
(iv)
(
√
34
+
√
106
+
√
113
)
(v)
(
√
34
+
√
109
+
113
)
Question
13
13.
Find the lengths of the sides of the triangle formed by the points
(
5
,
(
−
7
)
)
,
(
(
−
8
)
,
2
)
and
(
(
−
6
)
,
0
)
(i)
5
4
√
10
,
2
√
2
,
√
170
(ii)
5
√
10
,
2
√
2
,
√
172
(iii)
5
√
10
,
2
√
2
,
√
170
(iv)
5
√
10
,
4
,
√
170
Question
14
14.
The points
(
(
−
1
)
,
(
−
1
)
)
,
(
4
,
(
−
2
)
)
and
(
(
3
2
+
1
2
√
3
)
,
(
−
3
2
+
5
2
√
3
)
)
represent
(i)
isosceles triangle
(ii)
equilateral triangle
(iii)
right angled triangle
(iv)
scalene triangle
Question
15
15.
The points
(
(
−
5
)
,
(
−
1
)
)
,
(
(
−
2
)
,
2
)
and
(
1
,
(
−
1
)
)
represent
(i)
right angle triangle
(ii)
equilateral triangle
(iii)
collinear points
(iv)
scalene triangle
(v)
isosceles right angled triangle
Question
16
16.
The points
(
(
−
6
)
,
(
−
5
)
)
,
(
1
,
(
−
5
)
)
and
(
1
,
(
−
2
)
)
represent
(i)
isosceles right angled triangle
(ii)
scalene triangle
(iii)
collinear points
(iv)
equilateral triangle
(v)
right angle triangle
Question
17
17.
Distance of the point (2,8) from x-axis is
(i)
10
(ii)
(
−
6
)
(iii)
8
(iv)
6
(v)
2
Question
18
18.
Distance of the point (4,6) from y-axis is
(i)
(
−
2
)
(ii)
2
(iii)
4
(iv)
10
(v)
6
Question
19
19.
Distance of the given point from x-axis is
(i)
6
(ii)
0
(iii)
-6
Question
20
20.
Distance of the given point from y-axis is
(i)
2
(ii)
8
(iii)
4
(iv)
6
Question
21
21.
A point lies on positive side of x-axis at a distance of 4 units from y-axis. What are the coordinates of the point?
(i)
(
(
−
4
)
,
0
)
(ii)
(
0
,
(
−
4
)
)
(iii)
(
4
,
0
)
(iv)
(
0
,
4
)
Question
22
22.
A point lies on negative 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
23
23.
A point lies on positive side of y-axis at a distance of 8 units from x-axis. What are the coordinates of the point?
(i)
(
(
−
8
)
,
0
)
(ii)
(
0
,
8
)
(iii)
(
0
,
(
−
8
)
)
(iv)
(
8
,
0
)
Question
24
24.
A point lies on negative 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)
(
0
,
5
)
(iv)
(
(
−
5
)
,
0
)
Question
25
25.
Find the distance of the point
(
(
−
1
)
,
(
−
3
)
)
from origin
(i)
4
√
10
(ii)
√
13
(iii)
10
(iv)
√
10
(v)
√
8
Question
26
26.
A is a point on x-axis with abscissa
4
and B is a point on y-axis
with ordinate
6
.
Find the distance between A and B
(i)
2
4
√
13
(ii)
2
√
16
(iii)
2
√
13
(iv)
26
(v)
2
√
10
Question
27
27.
KM is the straight line of length
√
34
units.
If K has the coordinates
(
1
,
(
−
1
)
)
and M has coordinates
(k,-6)
,
find the possible values of k
(i)
(
6
,
0
)
(ii)
(
3
,
(
−
1
)
)
(iii)
(
5
,
(
−
3
)
)
(iv)
(
2
,
(
−
4
)
)
(v)
(
4
,
(
−
2
)
)
Question
28
28.
Find the point on x-axis which is equidistant
from the points
(
(
−
3
)
,
7
)
and
(
4
,
(
−
6
)
)
(i)
(
(
−
10
7
)
,
1
)
(ii)
(
11
7
,
2
)
(iii)
(
(
−
17
7
)
,
(
−
2
)
)
(iv)
(
(
−
3
7
)
,
0
)
(v)
(
4
7
,
(
−
1
)
)
Question
29
29.
Find the point on y-axis which is equidistant
from the points
(
3
,
7
)
and
(
(
−
1
)
,
(
−
2
)
)
(i)
(
(
−
1
)
,
71
18
)
(ii)
(
(
−
2
)
,
17
18
)
(iii)
(
1
,
35
18
)
(iv)
(
2
,
89
18
)
(v)
(
0
,
53
18
)
Question
30
30.
Find the points on x-axis,
which are at a distance of
14
units
from the point
(
(
−
1
)
,
(
−
8
)
)
(i)
(
(
−
3
+
2
√
33
)
,
(
−
2
)
)
,
(
(
−
1
−
2
√
33
)
,
0
)
(ii)
(
(
−
1
+
2
√
33
)
,
0
)
,
(
(
−
2
−
2
√
33
)
,
1
)
(iii)
(
(
−
1
+
2
√
33
)
,
0
)
,
(
(
−
1
−
2
√
33
)
,
0
)
(iv)
(
(
1
+
2
√
33
)
,
2
)
,
(
(
−
1
−
2
√
33
)
,
0
)
(v)
(
2
√
33
,
(
−
1
)
)
,
(
(
−
1
−
2
√
33
)
,
0
)
Question
31
31.
Find the points on y-axis,
which are at a distance of
13
units
from the point
(
(
−
8
)
,
2
)
(i)
(
2
,
(
4
+
√
105
)
)
,
(
0
,
(
2
−
√
105
)
)
(ii)
(
0
,
(
2
+
√
105
)
)
,
(
(
−
1
)
,
(
3
−
√
105
)
)
(iii)
(
(
−
2
)
,
√
105
)
,
(
0
,
(
2
−
√
105
)
)
(iv)
(
0
,
(
2
+
√
105
)
)
,
(
0
,
(
2
−
√
105
)
)
(v)
(
1
,
(
1
+
√
105
)
)
,
(
0
,
(
2
−
√
105
)
)
Question
32
32.
Find the lengths of the medians of a triangle whose vertices are
(
1
,
8
)
,
(
8
,
5
)
and
(
2
,
7
)
(i)
√
10
,
1
2
√
2
,
1
2
√
58
(ii)
2
√
5
,
1
2
√
194
,
1
2
√
26
(iii)
1
2
√
58
,
√
10
,
√
10
Question
33
33.
If point P
(x,7)
is equidistant from the points
(
(
−
4
)
,
(
−
2
)
)
and
(
7
,
7
)
, find x
(i)
(
-26
11
)
(ii)
-2
(iii)
(
-20
9
)
(iv)
(
-24
11
)
(v)
(
-28
13
)
Question
34
34.
If point P
(
97
6
,
3
)
is equidistant from the points
(a,-8)
and
(
(
−
4
)
,
6
)
, find a
(i)
1
(ii)
0
(iii)
-3
(iv)
-2
(v)
-1
Question
35
35.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
3
,
3
)
and
(
8
,
(
−
1
)
)
(i)
(
3
x
−
2
y
−
3
)
=
0
(ii)
(
−
11
x
+
8
y
+
47
)
=
0
(iii)
(
−
10
x
+
8
y
+
47
)
=
0
(iv)
(
−
10
x
+
10
y
+
47
)
=
0
(v)
(
3
x
−
4
y
−
3
)
=
0
Assignment Key
1) (iii)
2) (iv)
3) (iv)
4) (ii)
5) (iv)
6) (iv)
7) (ii)
8) (iii)
9) (iv)
10) (iv)
11) (iv)
12) (ii)
13) (iii)
14) (ii)
15) (v)
16) (v)
17) (iii)
18) (iii)
19) (ii)
20) (iii)
21) (iii)
22) (iii)
23) (ii)
24) (i)
25) (iv)
26) (iii)
27) (v)
28) (iv)
29) (v)
30) (iii)
31) (iv)
32) (ii)
33) (iv)
34) (v)
35) (iii)
