EduSahara™ Assignment
Name : Section Formula
Chapter : Coordinate Geometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
The mid-point of the join of points
(
1
,
1
)
and
(
(
−
8
)
,
(
−
8
)
)
is
(i)
(
(
−
7
2
)
,
(
−
7
2
)
)
(ii)
(
(
−
11
2
)
,
(
−
11
2
)
)
(iii)
(
(
−
3
2
)
,
(
−
3
2
)
)
(iv)
(
(
−
5
2
)
,
(
−
9
2
)
)
(v)
(
(
−
9
2
)
,
(
−
5
2
)
)
Question
2
2.
Find the point that divides the join of points
(
(
−
4
)
,
(
−
7
)
)
and
(
3
,
(
−
1
)
)
internally
in the ratio
2
:
2
(i)
(
(
−
5
2
)
,
(
−
6
)
)
(ii)
(
1
2
,
(
−
5
)
)
(iii)
(
(
−
1
2
)
,
(
−
4
)
)
(iv)
(
3
2
,
(
−
2
)
)
(v)
(
(
−
3
2
)
,
(
−
3
)
)
Question
3
3.
Find the coordinates of the mid points of the sides of the triangle formed by
(
2
,
(
−
5
)
)
,
(
(
−
1
)
,
8
)
and
(
5
,
2
)
(i)
(
1
2
,
3
2
)
,
(
2
,
5
)
,
(
7
2
,
(
−
3
2
)
)
(ii)
(
(
−
1
2
)
,
5
2
)
,
(
2
,
5
)
,
(
7
2
,
(
−
3
2
)
)
(iii)
(
1
2
,
3
2
)
,
(
4
,
7
)
,
(
7
2
,
(
−
3
2
)
)
(iv)
(
1
2
,
3
2
)
,
(
2
,
5
)
,
(
9
2
,
(
−
5
2
)
)
(v)
(
1
2
,
3
2
)
,
(
2
,
5
)
,
(
3
2
,
(
−
7
2
)
)
Question
4
4.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
(
−
5
2
)
,
9
2
)
,
(
(
−
7
2
)
,
4
)
and
(
(
−
2
)
,
15
2
)
(i)
(
(
−
1
)
,
8
)
,
(
(
−
4
)
,
1
)
,
(
(
−
3
)
,
7
)
(ii)
(
(
−
1
)
,
8
)
,
(
(
−
4
)
,
1
)
,
(
(
−
5
)
,
5
)
(iii)
(
(
−
1
)
,
8
)
,
(
(
−
2
)
,
3
)
,
(
(
−
3
)
,
7
)
(iv)
(
(
−
2
)
,
9
)
,
(
(
−
4
)
,
1
)
,
(
(
−
3
)
,
7
)
(v)
(
(
−
1
)
,
8
)
,
(
(
−
4
)
,
1
)
,
(
(
−
2
)
,
6
)
Question
5
5.
The mid-point of the join of the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is
(i)
(
x
1
+
x
2
3
,
y
1
+
y
2
3
)
(ii)
(
y
1
−
y
2
2
,
x
1
−
x
2
2
)
(iii)
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(iv)
(
x
1
−
x
2
2
,
y
1
−
y
2
2
)
(v)
(
x
1
−
x
2
3
,
y
1
−
y
2
3
)
Question
6
6.
The coordinates of the point dividing the join of points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
internally in the ratio m:n are
(i)
(
n
x
2
−
m
x
1
m - n
,
n
y
2
−
m
y
1
m - n
)
(ii)
(
m
x
2
−
n
x
1
m - n
,
m
y
2
−
n
y
1
m - n
)
(iii)
(
n
x
2
+
m
x
1
m + n
,
n
y
2
+
m
y
1
m + n
)
(iv)
(
m
x
2
+
n
x
1
m + n
,
m
y
2
+
n
y
1
m + n
)
Question
7
7.
If the point
(
(
−
7
)
,
12
7
)
divides the join of points
(
(
−
7
)
,
(
−
3
)
)
and
(
x
,
y
)
in the ratio
6
:
8
, find
(
x
,
y
)
(i)
(
(
−
9
)
,
6
)
(ii)
(
(
−
5
)
,
10
)
(iii)
(
(
−
7
)
,
8
)
(iv)
(
(
−
8
)
,
9
)
(v)
(
(
−
6
)
,
7
)
Question
8
8.
Find the ratio in which point
(
(
−
14
3
)
,
(
−
20
9
)
)
divides the join of points
(
(
−
5
)
,
(
−
3
)
)
and
(
(
−
2
)
,
4
)
(i)
1
:
6
(ii)
0
:
8
(iii)
1
:
8
(iv)
2
:
8
(v)
1
:
11
Question
9
9.
One end of the diameter of a circle is
(
6
,
5
)
.
If the centre is
(
4
,
7
2
)
,
find the other end of the diameter
(i)
(
2
,
2
)
(ii)
(
0
,
0
)
(iii)
(
1
,
3
)
(iv)
(
3
,
1
)
(v)
(
4
,
4
)
Question
10
10.
Find the coordinates of the points of trisection of the line segment
joining the points
(
6
,
(
−
8
)
)
and
(
2
,
(
−
7
)
)
(i)
(
20
3
,
(
−
17
3
)
)
,
(
10
3
,
(
−
22
3
)
)
(ii)
(
14
3
,
(
−
23
3
)
)
,
(
10
3
,
(
−
22
3
)
)
(iii)
(
14
3
,
(
−
23
3
)
)
,
(
7
3
,
(
−
19
3
)
)
(iv)
(
8
3
,
(
−
29
3
)
)
,
(
10
3
,
(
−
22
3
)
)
(v)
(
17
3
,
(
−
26
3
)
)
,
(
10
3
,
(
−
22
3
)
)
Question
11
11.
In what ratio is the join of
(
(
−
8
)
,
7
)
and
(
(
−
8
)
,
(
−
5
)
)
divided by x-axis?
(i)
2
:
9
(ii)
7
:
5
(iii)
2
:
4
(iv)
6
:
5
(v)
8
:
5
Question
12
12.
In what ratio is the join of
(
2
,
(
−
4
)
)
and
(
(
−
3
)
,
3
)
divided by y-axis?
(i)
2
:
3
(ii)
3
:
2
(iii)
2
:
1
(iv)
2
:
5
(v)
1
:
2
Question
13
13.
The centre of a circle is
(
5
2
,
5
2
)
.
Find the other end of the diameter whose one end point is
(
4
,
(
−
2
)
)
(i)
(
1
,
(
−
7
)
)
(ii)
(
7
,
1
)
(iii)
(
(
−
1
)
,
(
−
7
)
)
(iv)
(
1
,
7
)
(v)
(
(
−
1
)
,
7
)
Question
14
14.
Find the coordinates of the midpoints of the sides of the quadrilateral
formed by
(
(
−
1
)
,
(
−
2
)
)
,
(
4
,
2
)
,
(
(
−
1
)
,
4
)
and
(
(
−
2
)
,
2
)
(i)
(
7
2
,
2
)
,
(
3
2
,
3
)
,
(
(
−
3
2
)
,
3
)
,
(
(
−
3
2
)
,
0
)
(ii)
(
3
2
,
0
)
,
(
3
2
,
3
)
,
(
(
−
7
2
)
,
1
)
,
(
(
−
3
2
)
,
0
)
(iii)
(
3
2
,
0
)
,
(
3
2
,
3
)
,
(
(
−
3
2
)
,
3
)
,
(
(
−
5
2
)
,
1
)
(iv)
(
3
2
,
0
)
,
(
3
2
,
3
)
,
(
(
−
1
2
)
,
2
)
,
(
(
−
3
2
)
,
0
)
(v)
(
3
2
,
0
)
,
(
3
2
,
3
)
,
(
(
−
3
2
)
,
3
)
,
(
(
−
3
2
)
,
0
)
Question
15
15.
Find the point that bisects
(
0
,
(
−
6
)
)
and
(
6
,
(
−
3
)
)
(i)
(
4
,
(
−
11
2
)
)
(ii)
(
3
,
(
−
9
2
)
)
(iii)
(
5
,
(
−
5
2
)
)
(iv)
(
1
,
(
−
13
2
)
)
(v)
(
2
,
(
−
7
2
)
)
Question
16
16.
If point P
(
(
−
5
2
)
,
(
−
3
)
)
bisects A
(
(
−
5
)
,
(
−
7
)
)
and B
(
x
,
y
)
, find
(
x
,
y
)
(i)
(
0
,
1
)
(ii)
(
2
,
3
)
(iii)
(
(
−
1
)
,
2
)
(iv)
(
1
,
0
)
(v)
(
(
−
2
)
,
(
−
1
)
)
Question
17
17.
In what ratio is the join of
(
(
−
4
)
,
(
−
8
)
)
and
(
6
,
2
)
divided by the line
(
−
y
−
2
)
=
0
?
(i)
7
:
4
(ii)
6
:
4
(iii)
6
:
2
(iv)
6
:
7
(v)
5
:
4
Question
18
18.
In what ratio is the join of
(
(
−
4
)
,
(
−
1
)
)
and
(
2
,
5
)
divided by the line
(
x
+
2
)
=
0
?
(i)
2
:
4
(ii)
3
:
4
(iii)
1
:
4
(iv)
2
:
7
(v)
2
:
2
Question
19
19.
Three vertices of a parallelogram are
(
(
−
4
)
,
(
−
5
)
)
,
(
2
,
(
−
5
)
)
and
(
6
,
0
)
.
Find the fourth vertex
(i)
(
(
−
2
)
,
(
−
2
)
)
(ii)
(
0
,
0
)
(iii)
(
(
−
1
)
,
1
)
(iv)
(
2
,
2
)
(v)
(
1
,
(
−
1
)
)
Question
20
20.
Find the centre of the circle, the endpoints of whose
diameter are
(
(
−
6
)
,
(
−
8
)
)
and
(
(
−
1
)
,
1
)
(i)
(
(
−
7
2
)
,
7
2
)
(ii)
(
7
2
,
7
2
)
(iii)
(
(
−
7
2
)
,
(
−
7
2
)
)
(iv)
(
7
2
,
(
−
7
2
)
)
Question
21
21.
The line
(
10
x
+
4
y
+
39
)
=
0
bisects which of the following pairs of points?
(i)
(
1
,
(
−
5
)
)
,
(
(
−
5
)
,
(
−
6
)
)
(ii)
(
3
,
(
−
3
)
)
,
(
(
−
4
)
,
(
−
7
)
)
(iii)
(
2
,
(
−
6
)
)
,
(
(
−
4
)
,
(
−
7
)
)
(iv)
(
1
,
(
−
5
)
)
,
(
(
−
4
)
,
(
−
7
)
)
(v)
(
(
−
1
)
,
(
−
7
)
)
,
(
(
−
4
)
,
(
−
7
)
)
Question
22
22.
A and B are two points on the x-axis and y-axis respectively.
If
(
7
,
7
)
is the mid-point of the join of A and B, find A and B
(i)
(
14
,
0
)
,
(
0
,
14
)
(ii)
(
15
,
(
−
1
)
)
,
(
0
,
14
)
(iii)
(
12
,
(
−
2
)
)
,
(
0
,
14
)
(iv)
(
16
,
2
)
,
(
0
,
14
)
(v)
(
14
,
0
)
,
(
(
−
1
)
,
15
)
Assignment Key
1) (i)
2) (iii)
3) (i)
4) (i)
5) (iii)
6) (iv)
7) (iii)
8) (iii)
9) (i)
10) (ii)
11) (ii)
12) (i)
13) (iv)
14) (v)
15) (ii)
16) (i)
17) (ii)
18) (i)
19) (ii)
20) (iii)
21) (iv)
22) (i)
