EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
The centre of a circle is
(
9
2
,
1
2
)
.
Find the other end of the diameter whose one end point is
(
5
,
4
)
(i)
(
(
−
4
)
,
(
−
3
)
)
(ii)
(
(
−
4
)
,
3
)
(iii)
(
(
−
3
)
,
4
)
(iv)
(
4
,
3
)
(v)
(
4
,
(
−
3
)
)
Question
2
2.
Find the coordinates of the orthocentre of the triangle
whose vertices are
(
(
−
6
)
,
5
)
,
(
(
−
7
)
,
(
−
1
)
)
and
(
4
,
(
−
1
)
)
(i)
(
(
−
7
)
,
5
3
)
(ii)
(
(
−
4
)
,
8
3
)
(iii)
(
(
−
5
)
,
(
−
1
3
)
)
(iv)
(
(
−
6
)
,
2
3
)
(v)
(
(
−
8
)
,
(
−
4
3
)
)
Question
3
3.
The points
(
(
−
2
)
,
(
−
1
)
)
,
(
4
,
(
−
1
)
)
,
(
4
,
3
)
and
(
(
−
2
)
,
3
)
represents
(i)
rectangle
(ii)
rhombus
(iii)
parallelogram
(iv)
square
(v)
trapezium
Question
4
4.
A is a point on x-axis with abscissa
(-5)
and B is a point on y-axis
with ordinate
(-2)
.
Find the distance between A and B
(i)
√
31
(ii)
√
29
(iii)
29
(iv)
√
27
(v)
4
√
29
Question
5
5.
The points
(
7
,
(
−
1
)
)
,
(
5
,
(
−
1
)
)
and
(
1
,
(
−
8
)
)
represent
(i)
right angle triangle
(ii)
scalene triangle
(iii)
isosceles triangle
(iv)
collinear points
(v)
equilateral triangle
Question
6
6.
The points
(
3
,
4
)
,
(
6
,
5
)
and
(
(
9
2
−
1
2
√
3
)
,
(
9
2
+
3
2
√
3
)
)
represent
(i)
right angled triangle
(ii)
scalene triangle
(iii)
equilateral triangle
(iv)
isosceles triangle
Question
7
7.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
4
,
5
)
,
(
4
,
3
2
)
and
(
3
,
1
2
)
(i)
(
3
,
4
)
,
(
7
,
8
)
,
(
3
,
(
−
3
)
)
(ii)
(
3
,
4
)
,
(
5
,
6
)
,
(
4
,
(
−
4
)
)
(iii)
(
3
,
4
)
,
(
5
,
6
)
,
(
3
,
(
−
3
)
)
(iv)
(
3
,
4
)
,
(
5
,
6
)
,
(
1
,
(
−
5
)
)
(v)
(
2
,
5
)
,
(
5
,
6
)
,
(
3
,
(
−
3
)
)
Question
8
8.
Find the points on y-axis,
which are at a distance of
6
units
from the point
(
(
−
4
)
,
(
−
7
)
)
(i)
(
0
,
(
−
7
+
2
√
5
)
)
,
(
(
−
1
)
,
(
−
6
−
2
√
5
)
)
(ii)
(
0
,
(
−
7
+
2
√
5
)
)
,
(
0
,
(
−
7
−
2
√
5
)
)
(iii)
(
1
,
(
−
8
+
2
√
5
)
)
,
(
0
,
(
−
7
−
2
√
5
)
)
(iv)
(
(
−
2
)
,
(
−
9
+
2
√
5
)
)
,
(
0
,
(
−
7
−
2
√
5
)
)
(v)
(
2
,
(
−
5
+
2
√
5
)
)
,
(
0
,
(
−
7
−
2
√
5
)
)
Question
9
9.
Find the point which is equidistant from the points
(
0
,
(
−
3
)
)
,
(
(
−
6
)
,
7
)
and
(
(
−
7
)
,
0
)
(i)
(
(
−
69
26
)
,
99
26
)
(ii)
(
(
−
95
26
)
,
21
26
)
(iii)
(
9
26
,
125
26
)
(iv)
(
(
−
17
26
)
,
47
26
)
(v)
(
(
−
43
26
)
,
73
26
)
Question
10
10.
Distance of the point (7,2) from x-axis is
(i)
7
(ii)
2
(iii)
5
(iv)
(
−
5
)
(v)
9
Question
11
11.
The mid-point of the join of points
(
(
−
2
)
,
7
)
and
(
5
,
(
−
8
)
)
is
(i)
(
5
2
,
(
−
3
2
)
)
(ii)
(
1
2
,
1
2
)
(iii)
(
7
2
,
3
2
)
(iv)
(
3
2
,
(
−
1
2
)
)
(v)
(
(
−
1
2
)
,
(
−
5
2
)
)
Question
12
12.
Find the point that bisects
(
2
,
2
)
and
(
(
−
3
)
,
2
)
(i)
(
(
−
3
2
)
,
3
)
(ii)
(
1
2
,
1
)
(iii)
(
(
−
1
2
)
,
2
)
(iv)
(
(
−
5
2
)
,
0
)
(v)
(
3
2
,
4
)
Question
13
13.
Find the centre of the circle, the endpoints of whose
diameter are
(
8
,
8
)
and
(
(
−
2
)
,
5
)
(i)
(
3
,
13
2
)
(ii)
(
3
,
(
−
13
2
)
)
(iii)
(
(
−
3
)
,
13
2
)
(iv)
(
(
−
3
)
,
(
−
13
2
)
)
(v)
(
13
2
,
3
)
Question
14
14.
The points
(
(
−
1
)
,
(
−
4
)
)
,
(
5
,
(
−
4
)
)
,
(
7
,
0
)
and
(
1
,
0
)
represent
(i)
rectangle
(ii)
rhombus
(iii)
trapezium
(iv)
square
(v)
parallelogram
Question
15
15.
The centroid of the triangle formed by the points
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
and
(
x
3
,
y
3
)
is
(i)
(
x
1
−
x
2
−
x
3
2
,
y
1
−
y
2
−
y
3
2
)
(ii)
(
x
1
−
x
2
−
x
3
3
,
y
1
−
y
2
−
y
3
3
)
(iii)
(
y
1
−
y
2
−
y
3
2
,
x
1
−
x
2
−
x
3
2
)
(iv)
(
y
1
+
y
2
+
y
3
2
,
x
1
+
x
2
+
x
3
2
)
(v)
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
)
Question
16
16.
Find the relation between x and y if the points
(
x
,
y
)
,
(
3
,
(
−
8
)
)
and
(
(
−
1
)
,
(
−
1
)
)
are collinear
(i)
(
2
y
+
16
)
=
0
(ii)
(
14
x
−
6
y
−
62
)
=
0
(iii)
(
7
x
−
8
y
−
1
)
=
0
(iv)
(
−
7
x
−
2
y
−
9
)
=
0
(v)
(
7
x
+
4
y
+
11
)
=
0
Question
17
17.
In what ratio is the join of
(
8
,
3
)
and
(
(
−
1
)
,
0
)
divided by y-axis?
(i)
5
:
6
(ii)
8
:
-1
(iii)
8
:
4
(iv)
3
:
6
(v)
8
:
1
Question
18
18.
A point lies on negative side of x-axis at a distance of 2 units from y-axis. What are the coordinates of the point?
(i)
(
(
−
2
)
,
0
)
(ii)
(
2
,
0
)
(iii)
(
0
,
2
)
(iv)
(
0
,
(
−
2
)
)
Question
19
19.
A and B are two points on the x-axis and y-axis respectively.
If
(
(
−
3
)
,
8
)
is the mid-point of the join of A and B, find A and B
(i)
(
(
−
6
)
,
0
)
,
(
(
−
1
)
,
17
)
(ii)
(
(
−
6
)
,
0
)
,
(
0
,
16
)
(iii)
(
(
−
4
)
,
2
)
,
(
0
,
16
)
(iv)
(
(
−
8
)
,
(
−
2
)
)
,
(
0
,
16
)
(v)
(
(
−
5
)
,
(
−
1
)
)
,
(
0
,
16
)
Question
20
20.
The points
(
(
−
5
)
,
(
−
5
)
)
,
(
1
,
(
−
5
)
)
and
(
1
,
0
)
represent
(i)
isosceles right angled triangle
(ii)
equilateral triangle
(iii)
right angle triangle
(iv)
collinear points
(v)
scalene triangle
Question
21
21.
Three vertices of a parallelogram are
(
(
−
3
)
,
(
−
2
)
)
,
(
4
,
(
−
2
)
)
and
(
7
,
3
)
.
Find the fourth vertex
(i)
(
(
−
1
)
,
4
)
(ii)
(
1
,
2
)
(iii)
(
(
−
2
)
,
1
)
(iv)
(
0
,
3
)
(v)
(
2
,
5
)
Question
22
22.
A point lies on negative side of y-axis at a distance of 8 units from x-axis. What are the coordinates of the point?
(i)
(
0
,
(
−
8
)
)
(ii)
(
0
,
8
)
(iii)
(
(
−
8
)
,
0
)
(iv)
(
8
,
0
)
Question
23
23.
Find the distance between the points
(
(
−
4
)
,
5
)
and
(
4
,
1
)
(i)
4
√
5
(ii)
4
√
7
(iii)
20
(iv)
4
√
2
(v)
4
4
√
5
Question
24
24.
The points
(
(
−
3
)
,
0
)
,
(
(
−
5
)
,
7
)
and
(
(
−
25
2
)
,
15
14
)
represent
(i)
scalene triangle
(ii)
collinear points
(iii)
isosceles triangle
(iv)
equilateral triangle
(v)
right angle triangle
Question
25
25.
The points B
(
(
−
2
)
,
6
)
and D
(
(
−
8
)
,
6
)
are the opposite vertices
of a square ABCD. Find the other two vertices
(i)
(
(
−
4
)
,
2
)
,
(
(
−
5
)
,
9
)
(ii)
(
(
−
3
)
,
5
)
,
(
(
−
5
)
,
9
)
(iii)
(
(
−
7
)
,
1
)
,
(
(
−
5
)
,
9
)
(iv)
(
(
−
5
)
,
3
)
,
(
(
−
6
)
,
10
)
(v)
(
(
−
5
)
,
3
)
,
(
(
−
5
)
,
9
)
Assignment Key
1) (v)
2) (iv)
3) (i)
4) (ii)
5) (ii)
6) (iii)
7) (iii)
8) (ii)
9) (v)
10) (ii)
11) (iv)
12) (iii)
13) (i)
14) (v)
15) (v)
16) (v)
17) (v)
18) (i)
19) (ii)
20) (iii)
21) (iv)
22) (i)
23) (i)
24) (iii)
25) (v)
