EduSahara™ Assignment
Name : Section Formula
Chapter : Coordinate Geometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The mid-point of the join of points
(
(
−
7
)
,
(
−
1
)
)
and
(
3
,
8
)
is
(i)
(
(
−
2
)
,
7
2
)
(ii)
(
0
,
11
2
)
(iii)
(
(
−
4
)
,
3
2
)
(iv)
(
(
−
1
)
,
5
2
)
(v)
(
(
−
3
)
,
9
2
)
Question
2
2.
Find the point that divides the join of points
(
(
−
7
)
,
(
−
5
)
)
and
(
(
−
7
)
,
7
)
internally
in the ratio
6
:
4
(i)
(
(
−
7
)
,
11
5
)
(ii)
(
(
−
6
)
,
6
5
)
(iii)
(
(
−
5
)
,
21
5
)
(iv)
(
(
−
8
)
,
16
5
)
(v)
(
(
−
9
)
,
1
5
)
Question
3
3.
Find the centroid of the triangle formed by the points
(
0
,
(
−
3
)
)
,
(
(
−
5
)
,
(
−
6
)
)
and
(
(
−
5
)
,
(
−
3
)
)
(i)
(
(
−
7
3
)
,
(
−
5
)
)
(ii)
(
(
−
10
3
)
,
(
−
4
)
)
(iii)
(
(
−
16
3
)
,
(
−
6
)
)
(iv)
(
(
−
4
3
)
,
(
−
2
)
)
(v)
(
(
−
13
3
)
,
(
−
3
)
)
Question
4
4.
Find the coordinates of the mid points of the sides of the triangle formed by
(
4
,
7
)
,
(
1
,
(
−
3
)
)
and
(
(
−
7
)
,
(
−
2
)
)
(i)
(
3
2
,
3
)
,
(
(
−
3
)
,
(
−
5
2
)
)
,
(
(
−
3
2
)
,
5
2
)
(ii)
(
5
2
,
2
)
,
(
(
−
1
)
,
(
−
1
2
)
)
,
(
(
−
3
2
)
,
5
2
)
(iii)
(
5
2
,
2
)
,
(
(
−
3
)
,
(
−
5
2
)
)
,
(
(
−
7
2
)
,
1
2
)
(iv)
(
5
2
,
2
)
,
(
(
−
3
)
,
(
−
5
2
)
)
,
(
(
−
1
2
)
,
3
2
)
(v)
(
5
2
,
2
)
,
(
(
−
3
)
,
(
−
5
2
)
)
,
(
(
−
3
2
)
,
5
2
)
Question
5
5.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
(
−
7
2
)
,
(
−
5
2
)
)
,
(
3
2
,
(
−
5
2
)
)
and
(
2
,
(
−
7
)
)
(i)
(
(
−
3
)
,
(
−
7
)
)
,
(
(
−
4
)
,
2
)
,
(
8
,
(
−
8
)
)
(ii)
(
(
−
3
)
,
(
−
7
)
)
,
(
(
−
2
)
,
4
)
,
(
7
,
(
−
7
)
)
(iii)
(
(
−
3
)
,
(
−
7
)
)
,
(
(
−
4
)
,
2
)
,
(
5
,
(
−
9
)
)
(iv)
(
(
−
4
)
,
(
−
6
)
)
,
(
(
−
4
)
,
2
)
,
(
7
,
(
−
7
)
)
(v)
(
(
−
3
)
,
(
−
7
)
)
,
(
(
−
4
)
,
2
)
,
(
7
,
(
−
7
)
)
Question
6
6.
The mid-point of the join of the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is
(i)
(
x
1
−
x
2
2
,
y
1
−
y
2
2
)
(ii)
(
x
1
+
x
2
3
,
y
1
+
y
2
3
)
(iii)
(
x
1
−
x
2
3
,
y
1
−
y
2
3
)
(iv)
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(v)
(
y
1
−
y
2
2
,
x
1
−
x
2
2
)
Question
7
7.
The centroid of the triangle formed by the points
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
and
(
x
3
,
y
3
)
is
(i)
(
y
1
+
y
2
+
y
3
2
,
x
1
+
x
2
+
x
3
2
)
(ii)
(
y
1
−
y
2
−
y
3
2
,
x
1
−
x
2
−
x
3
2
)
(iii)
(
x
1
−
x
2
−
x
3
2
,
y
1
−
y
2
−
y
3
2
)
(iv)
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
)
(v)
(
x
1
−
x
2
−
x
3
3
,
y
1
−
y
2
−
y
3
3
)
Question
8
8.
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)
(
n
x
2
−
m
x
1
m - n
,
n
y
2
−
m
y
1
m - n
)
(iii)
(
m
x
2
+
n
x
1
m + n
,
m
y
2
+
n
y
1
m + n
)
(iv)
(
m
x
2
−
n
x
1
m - n
,
m
y
2
−
n
y
1
m - n
)
Question
9
9.
If the point
(
11
2
,
43
12
)
divides the join of points
(
2
,
3
)
and
(
x
,
y
)
in the ratio
7
:
5
, find
(
x
,
y
)
(i)
(
10
,
6
)
(ii)
(
9
,
3
)
(iii)
(
6
,
2
)
(iv)
(
7
,
5
)
(v)
(
8
,
4
)
Question
10
10.
Find the ratio in which point
(
(
−
1
2
)
,
(
−
11
2
)
)
divides the join of points
(
3
,
(
−
6
)
)
and
(
(
−
4
)
,
(
−
5
)
)
(i)
8
:
7
(ii)
7
:
9
(iii)
7
:
4
(iv)
6
:
7
(v)
7
:
7
Question
11
11.
One end of the diameter of a circle is
(
(
−
6
)
,
5
)
.
If the centre is
(
(
−
13
2
)
,
1
2
)
,
find the other end of the diameter
(i)
(
(
−
9
)
,
(
−
6
)
)
(ii)
(
(
−
7
)
,
(
−
4
)
)
(iii)
(
(
−
5
)
,
(
−
2
)
)
(iv)
(
(
−
6
)
,
(
−
5
)
)
(v)
(
(
−
8
)
,
(
−
3
)
)
Question
12
12.
Find the coordinates of the points of trisection of the line segment
joining the points
(
(
−
6
)
,
6
)
and
(
5
,
6
)
(i)
(
(
−
4
3
)
,
5
)
,
(
4
3
,
6
)
(ii)
(
(
−
1
3
)
,
8
)
,
(
4
3
,
6
)
(iii)
(
(
−
13
3
)
,
4
)
,
(
4
3
,
6
)
(iv)
(
(
−
7
3
)
,
6
)
,
(
4
3
,
6
)
(v)
(
(
−
7
3
)
,
6
)
,
(
1
3
,
7
)
Question
13
13.
In what ratio is the join of
(
(
−
1
)
,
5
)
and
(
7
,
(
−
9
)
)
divided by x-axis?
(i)
2
:
8
(ii)
4
:
9
(iii)
5
:
9
(iv)
2
:
3
(v)
6
:
9
Question
14
14.
In what ratio is the join of
(
2
,
0
)
and
(
(
−
2
)
,
4
)
divided by y-axis?
(i)
5
:
3
(ii)
2
:
2
(iii)
2
:
5
(iv)
2
:
-1
(v)
7
:
3
Question
15
15.
Two vertices of a triangle are
(
(
−
3
)
,
2
)
,
(
4
,
2
)
and its centriod is
(
3
,
1
)
. Find the coordinates of the third vertex of the triangle
(i)
(
(
−
1
)
,
8
)
(ii)
(
(
−
8
)
,
1
)
(iii)
(
(
−
8
)
,
(
−
1
)
)
(iv)
(
8
,
1
)
(v)
(
8
,
(
−
1
)
)
Question
16
16.
The centre of a circle is
(
5
2
,
6
)
.
Find the other end of the diameter whose one end point is
(
(
−
1
)
,
5
)
(i)
(
(
−
6
)
,
7
)
(ii)
(
6
,
(
−
7
)
)
(iii)
(
(
−
6
)
,
(
−
7
)
)
(iv)
(
7
,
6
)
(v)
(
6
,
7
)
Question
17
17.
Find the coordinates of the midpoints of the sides of the quadrilateral
formed by
(
(
−
2
)
,
(
−
6
)
)
,
(
1
,
(
−
3
)
)
,
(
(
−
2
)
,
(
−
2
)
)
and
(
(
−
3
)
,
(
−
4
)
)
(i)
(
(
−
1
2
)
,
(
−
9
2
)
)
,
(
(
−
1
2
)
,
(
−
5
2
)
)
,
(
(
−
5
2
)
,
(
−
3
)
)
,
(
(
−
5
2
)
,
(
−
5
)
)
(ii)
(
(
−
1
2
)
,
(
−
9
2
)
)
,
(
(
−
1
2
)
,
(
−
5
2
)
)
,
(
(
−
9
2
)
,
(
−
5
)
)
,
(
(
−
5
2
)
,
(
−
5
)
)
(iii)
(
(
−
1
2
)
,
(
−
9
2
)
)
,
(
(
−
1
2
)
,
(
−
5
2
)
)
,
(
(
−
3
2
)
,
(
−
4
)
)
,
(
(
−
5
2
)
,
(
−
5
)
)
(iv)
(
(
−
1
2
)
,
(
−
9
2
)
)
,
(
(
−
1
2
)
,
(
−
5
2
)
)
,
(
(
−
5
2
)
,
(
−
3
)
)
,
(
(
−
7
2
)
,
(
−
4
)
)
(v)
(
3
2
,
(
−
5
2
)
)
,
(
(
−
1
2
)
,
(
−
5
2
)
)
,
(
(
−
5
2
)
,
(
−
3
)
)
,
(
(
−
5
2
)
,
(
−
5
)
)
Question
18
18.
Find the lengths of the medians of a triangle whose vertices are
(
1
,
(
−
2
)
)
,
(
(
−
3
)
,
(
−
6
)
)
and
(
(
−
2
)
,
3
)
(i)
1
2
√
82
,
1
2
√
34
,
2
√
2
(ii)
5
2
√
2
,
1
2
√
194
,
5
√
2
(iii)
2
√
2
,
1
2
√
82
,
1
2
√
82
Question
19
19.
Find the point that bisects
(
(
−
2
)
,
(
−
6
)
)
and
(
(
−
6
)
,
5
)
(i)
(
(
−
2
)
,
3
2
)
(ii)
(
(
−
3
)
,
(
−
3
2
)
)
(iii)
(
(
−
4
)
,
(
−
1
2
)
)
(iv)
(
(
−
6
)
,
(
−
5
2
)
)
(v)
(
(
−
5
)
,
1
2
)
Question
20
20.
If point P
(
4
,
5
)
bisects A
(
8
,
7
)
and B
(
x
,
y
)
, find
(
x
,
y
)
(i)
(
(
−
1
)
,
4
)
(ii)
(
(
−
2
)
,
1
)
(iii)
(
2
,
5
)
(iv)
(
1
,
2
)
(v)
(
0
,
3
)
Question
21
21.
Three vertices of a parallelogram are
(
(
−
6
)
,
(
−
2
)
)
,
(
1
,
(
−
2
)
)
and
(
4
,
1
)
.
Find the fourth vertex
(i)
(
(
−
3
)
,
1
)
(ii)
(
(
−
5
)
,
(
−
1
)
)
(iii)
(
(
−
1
)
,
3
)
(iv)
(
(
−
2
)
,
0
)
(v)
(
(
−
4
)
,
2
)
Question
22
22.
Find the centre of the circle, the endpoints of whose
diameter are
(
4
,
4
)
and
(
(
−
3
)
,
8
)
(i)
(
(
−
1
2
)
,
(
−
6
)
)
(ii)
(
(
−
1
2
)
,
6
)
(iii)
(
1
2
,
6
)
(iv)
(
1
2
,
(
−
6
)
)
(v)
(
6
,
1
2
)
Question
23
23.
The line
(
−
28
x
+
10
y
−
33
)
=
0
bisects which of the following pairs of points?
(i)
(
(
−
6
)
,
5
)
,
(
6
,
(
−
2
)
)
(ii)
(
(
−
8
)
,
3
)
,
(
5
,
(
−
1
)
)
(iii)
(
(
−
8
)
,
3
)
,
(
6
,
(
−
2
)
)
(iv)
(
(
−
7
)
,
2
)
,
(
6
,
(
−
2
)
)
(v)
(
(
−
10
)
,
1
)
,
(
6
,
(
−
2
)
)
Question
24
24.
A and B are two points on the x-axis and y-axis respectively.
If
(
(
−
8
)
,
1
)
is the mid-point of the join of A and B, find A and B
(i)
(
(
−
18
)
,
(
−
2
)
)
,
(
0
,
2
)
(ii)
(
(
−
14
)
,
2
)
,
(
0
,
2
)
(iii)
(
(
−
15
)
,
(
−
1
)
)
,
(
0
,
2
)
(iv)
(
(
−
16
)
,
0
)
,
(
0
,
2
)
(v)
(
(
−
16
)
,
0
)
,
(
(
−
1
)
,
3
)
Question
25
25.
If A
(
0
,
5
)
and B
(
1
,
7
)
are two points,
find the coordinates of the point C on AB produced so that AC = 2BC
(i)
(
1
,
10
)
(ii)
(
3
,
8
)
(iii)
(
2
,
9
)
(iv)
(
0
,
7
)
(v)
(
4
,
11
)
Assignment Key
1) (i)
2) (i)
3) (ii)
4) (v)
5) (v)
6) (iv)
7) (iv)
8) (iii)
9) (v)
10) (v)
11) (ii)
12) (iv)
13) (iii)
14) (ii)
15) (v)
16) (v)
17) (i)
18) (ii)
19) (iii)
20) (v)
21) (i)
22) (iii)
23) (iii)
24) (iv)
25) (iii)
