EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The points B
(
(
−
1
)
,
10
)
and D
(
(
−
9
)
,
10
)
are the opposite vertices
of a square ABCD. Find the other two vertices
(i)
(
(
−
4
)
,
5
)
,
(
(
−
5
)
,
14
)
(ii)
(
(
−
3
)
,
8
)
,
(
(
−
5
)
,
14
)
(iii)
(
(
−
5
)
,
6
)
,
(
(
−
5
)
,
14
)
(iv)
(
(
−
5
)
,
6
)
,
(
(
−
6
)
,
15
)
(v)
(
(
−
7
)
,
4
)
,
(
(
−
5
)
,
14
)
Question
2
2.
If point P
(
3
2
,
0
)
bisects A
(
5
,
(
−
8
)
)
and B
(
x
,
y
)
, find
(
x
,
y
)
(i)
(
(
−
3
)
,
9
)
(ii)
(
(
−
1
)
,
7
)
(iii)
(
(
−
2
)
,
8
)
(iv)
(
(
−
4
)
,
6
)
(v)
(
0
,
10
)
Question
3
3.
In what ratio is the join of
(
(
−
3
)
,
(
−
9
)
)
and
(
(
−
6
)
,
3
)
divided by the line
(
−
y
−
7
)
=
0
?
(i)
2
:
8
(ii)
2
:
10
(iii)
1
:
10
(iv)
2
:
12
(v)
3
:
10
Question
4
4.
If point P
(x,3)
is equidistant from the points
(
8
,
3
)
and
(
(
−
1
)
,
2
)
, find x
(i)
29
9
(ii)
25
7
(iii)
31
9
(iv)
37
11
(v)
11
3
Question
5
5.
Find the coordinates of the circumcentre of the triangle
whose vertices are
(
5
,
(
−
5
)
)
,
(
(
−
7
)
,
4
)
and
(
(
−
3
)
,
6
)
(i)
(
(
−
11
4
)
,
(
−
1
2
)
)
(ii)
(
1
4
,
1
2
)
(iii)
(
(
−
3
4
)
,
(
−
5
2
)
)
(iv)
(
(
−
15
4
)
,
(
−
7
2
)
)
(v)
(
(
−
7
4
)
,
(
−
3
2
)
)
Question
6
6.
If the point
(
1
3
,
34
9
)
divides the join of points
(
1
,
4
)
and
(
x
,
y
)
in the ratio
1
:
8
, find
(
x
,
y
)
(i)
(
(
−
7
)
,
0
)
(ii)
(
(
−
5
)
,
2
)
(iii)
(
(
−
4
)
,
1
)
(iv)
(
(
−
6
)
,
3
)
(v)
(
(
−
3
)
,
4
)
Question
7
7.
Find the circumradius of the triangle whose vertices are
(
(
−
2
)
,
(
−
1
)
)
,
(
6
,
(
−
5
)
)
and
(
(
−
5
)
,
4
)
(i)
1
7
√
8582
(ii)
1
7
√
8585
(iii)
8585
7
(iv)
1
7
4
√
8585
(v)
1
7
√
8588
Question
8
8.
If point P
(
(
−
49
4
)
,
6
)
is equidistant from the points
(a,7)
and
(
1
,
(
−
8
)
)
, find a
(i)
7
(ii)
5
(iii)
6
(iv)
8
(v)
9
Question
9
9.
Distance of the given point from x-axis is
(i)
2
(ii)
48
(iii)
6
(iv)
8
(v)
14
Question
10
10.
Find the area of the triangle
formed by the points
(
7
,
(
−
1
)
)
,
(
(
−
2
)
,
(
−
2
)
)
and
(
(
−
4
)
,
1
)
(i)
57
4
(ii)
27
2
(iii)
29
2
(iv)
31
2
(v)
15
Question
11
11.
Find the value of k such that the points
(
(
−
4
)
,
(
−
6
)
)
,
(
(
−
5
3
)
,
8
15
)
and
(1,k)
are collinear
(i)
5
(ii)
8
(iii)
11
(iv)
9
(v)
7
Question
12
12.
Find the value of k such that the points
(
(
−
6
)
,
3
)
,
(
(
−
42
13
)
,
51
13
)
and
(k,7)
are collinear
(i)
7
(ii)
6
(iii)
4
(iv)
5
(v)
8
Question
13
13.
Find the centre of the circle passing through
the points
(
(
−
4
)
,
1
)
,
(
(
−
6
)
,
5
)
and
(
(
−
8
)
,
3
)
(i)
(
(
−
20
3
)
,
11
3
)
(ii)
(
(
−
23
3
)
,
2
3
)
(iii)
(
(
−
14
3
)
,
5
3
)
(iv)
(
(
−
17
3
)
,
8
3
)
(v)
(
(
−
11
3
)
,
14
3
)
Question
14
14.
Find the lengths of the sides of the triangle formed by the points
(
4
,
1
)
,
(
3
,
1
)
and
(
(
−
4
)
,
7
)
(i)
1
,
√
85
,
12
(ii)
2
,
√
85
,
10
(iii)
1
,
85
,
10
(iv)
1
,
√
85
,
10
Question
15
15.
KM is the straight line of length
√
241
units.
If K has the coordinates
(
(
−
8
)
,
4
)
and M has coordinates
(k,8)
,
find the possible values of k
(i)
(
5
,
(
−
25
)
)
(ii)
(
6
,
(
−
22
)
)
(iii)
(
9
,
(
−
21
)
)
(iv)
(
8
,
(
−
24
)
)
(v)
(
7
,
(
−
23
)
)
Question
16
16.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
(
−
3
2
)
,
1
)
,
(
(
−
1
)
,
4
)
and
(
11
2
,
(
−
2
)
)
(i)
(
5
,
(
−
5
)
)
,
(
(
−
8
)
,
7
)
,
(
7
,
0
)
(ii)
(
4
,
(
−
4
)
)
,
(
(
−
8
)
,
7
)
,
(
6
,
1
)
(iii)
(
5
,
(
−
5
)
)
,
(
(
−
6
)
,
9
)
,
(
6
,
1
)
(iv)
(
5
,
(
−
5
)
)
,
(
(
−
8
)
,
7
)
,
(
6
,
1
)
(v)
(
5
,
(
−
5
)
)
,
(
(
−
8
)
,
7
)
,
(
4
,
(
−
1
)
)
Question
17
17.
A is a point on x-axis with abscissa
7
and B is a point on y-axis
with ordinate
0
.
Find the distance between A and B
(i)
10
(ii)
4
(iii)
6
(iv)
8
(v)
7
Question
18
18.
Find the point that bisects
(
4
,
(
−
7
)
)
and
(
(
−
1
)
,
(
−
5
)
)
(i)
(
3
2
,
(
−
6
)
)
(ii)
(
7
2
,
(
−
4
)
)
(iii)
(
5
2
,
(
−
7
)
)
(iv)
(
1
2
,
(
−
5
)
)
(v)
(
(
−
1
2
)
,
(
−
8
)
)
Question
19
19.
Find the relation between x and y if the points
(
x
,
y
)
,
(
4
,
8
)
and
(
7
,
(
−
7
)
)
are collinear
(i)
(
−
15
x
−
3
y
+
84
)
=
0
(ii)
(
−
13
x
−
5
y
+
14
)
=
0
(iii)
(
6
y
−
48
)
=
0
(iv)
(
15
x
+
9
y
−
42
)
=
0
(v)
(
2
x
+
4
y
+
14
)
=
0
Question
20
20.
Find the points on y-axis,
which are at a distance of
9
units
from the point
(
2
,
(
−
6
)
)
(i)
(
2
,
(
−
4
+
√
77
)
)
,
(
0
,
(
−
6
−
√
77
)
)
(ii)
(
0
,
(
−
6
+
√
77
)
)
,
(
(
−
1
)
,
(
−
5
−
√
77
)
)
(iii)
(
(
−
2
)
,
(
−
8
+
√
77
)
)
,
(
0
,
(
−
6
−
√
77
)
)
(iv)
(
0
,
(
−
6
+
√
77
)
)
,
(
0
,
(
−
6
−
√
77
)
)
(v)
(
1
,
(
−
7
+
√
77
)
)
,
(
0
,
(
−
6
−
√
77
)
)
Question
21
21.
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)
(
1
,
0
)
(iii)
(
0
,
(
−
1
)
)
(iv)
(
0
,
1
)
Question
22
22.
The points
(
(
−
1
)
,
(
−
1
)
)
,
(
6
,
(
−
1
)
)
,
(
6
,
4
)
and
(
(
−
1
)
,
4
)
represents
(i)
parallelogram
(ii)
square
(iii)
rectangle
(iv)
trapezium
(v)
rhombus
Question
23
23.
Find the coordinates of the midpoints of the sides of the quadrilateral
formed by
(
(
−
5
)
,
4
)
,
(
(
−
2
)
,
9
)
,
(
(
−
7
)
,
10
)
and
(
(
−
7
)
,
7
)
(i)
(
(
−
3
2
)
,
17
2
)
,
(
(
−
9
2
)
,
19
2
)
,
(
(
−
7
)
,
17
2
)
,
(
(
−
6
)
,
11
2
)
(ii)
(
(
−
7
2
)
,
13
2
)
,
(
(
−
9
2
)
,
19
2
)
,
(
(
−
9
)
,
13
2
)
,
(
(
−
6
)
,
11
2
)
(iii)
(
(
−
7
2
)
,
13
2
)
,
(
(
−
9
2
)
,
19
2
)
,
(
(
−
6
)
,
15
2
)
,
(
(
−
6
)
,
11
2
)
(iv)
(
(
−
7
2
)
,
13
2
)
,
(
(
−
9
2
)
,
19
2
)
,
(
(
−
7
)
,
17
2
)
,
(
(
−
6
)
,
11
2
)
(v)
(
(
−
7
2
)
,
13
2
)
,
(
(
−
9
2
)
,
19
2
)
,
(
(
−
7
)
,
17
2
)
,
(
(
−
7
)
,
13
2
)
Question
24
24.
The points
(
(
−
3
)
,
(
−
6
)
)
,
(
0
,
(
−
3
)
)
,
(
3
,
(
−
6
)
)
and
(
0
,
(
−
9
)
)
represent
(i)
parallelogram
(ii)
rhombus
(iii)
trapezium
(iv)
square
(v)
rectangle
Question
25
25.
Distance of the point (4,8) from x-axis is
(i)
4
(ii)
8
(iii)
(
−
4
)
(iv)
12
Assignment Key
1) (iii)
2) (iii)
3) (ii)
4) (iii)
5) (v)
6) (ii)
7) (ii)
8) (i)
9) (iv)
10) (iii)
11) (ii)
12) (ii)
13) (iv)
14) (iv)
15) (v)
16) (iv)
17) (v)
18) (i)
19) (i)
20) (iv)
21) (iii)
22) (iii)
23) (iv)
24) (iv)
25) (ii)
