EduSahara™ Assignment
Name : Section Formula
Chapter : Distance and Section Formulae
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Find the point that divides the join of points
(
(
−
5
)
,
1
)
and
(
6
,
2
)
internally
in the ratio
3
:
6
(i)
(
2
3
,
10
3
)
(ii)
(
(
−
10
3
)
,
(
−
2
3
)
)
(iii)
(
(
−
7
3
)
,
7
3
)
(iv)
(
(
−
1
3
)
,
1
3
)
(v)
(
(
−
4
3
)
,
4
3
)
Question
2
2.
Find the coordinates of the mid points of the sides of the triangle formed by
(
(
−
2
)
,
(
−
2
)
)
,
(
(
−
4
)
,
2
)
and
(
4
,
3
)
(i)
(
(
−
3
)
,
0
)
,
(
0
,
5
2
)
,
(
2
,
(
−
1
2
)
)
(ii)
(
(
−
3
)
,
0
)
,
(
0
,
5
2
)
,
(
1
,
1
2
)
(iii)
(
(
−
4
)
,
1
)
,
(
0
,
5
2
)
,
(
1
,
1
2
)
(iv)
(
(
−
3
)
,
0
)
,
(
0
,
5
2
)
,
(
(
−
1
)
,
(
−
3
2
)
)
(v)
(
(
−
3
)
,
0
)
,
(
2
,
9
2
)
,
(
1
,
1
2
)
Question
3
3.
Find the coordinates of the vertices of the triangle,
the mid points of whose sides are
(
5
2
,
1
2
)
,
(
1
,
1
)
and
(
(
−
3
2
)
,
(
−
5
2
)
)
(i)
(
(
−
1
)
,
(
−
2
)
)
,
(
5
,
4
)
,
(
(
−
3
)
,
(
−
2
)
)
(ii)
(
0
,
(
−
3
)
)
,
(
5
,
4
)
,
(
(
−
2
)
,
(
−
3
)
)
(iii)
(
0
,
(
−
3
)
)
,
(
5
,
4
)
,
(
(
−
3
)
,
(
−
2
)
)
(iv)
(
0
,
(
−
3
)
)
,
(
5
,
4
)
,
(
(
−
5
)
,
(
−
4
)
)
(v)
(
0
,
(
−
3
)
)
,
(
7
,
6
)
,
(
(
−
3
)
,
(
−
2
)
)
Question
4
4.
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)
(
m
x
2
−
n
x
1
m - n
,
m
y
2
−
n
y
1
m - n
)
(iv)
(
n
x
2
+
m
x
1
m + n
,
n
y
2
+
m
y
1
m + n
)
Question
5
5.
If the point
(
(
−
16
5
)
,
18
5
)
divides the join of points
(
(
−
4
)
,
6
)
and
(
x
,
y
)
in the ratio
1
:
4
, find
(
x
,
y
)
(i)
(
(
−
2
)
,
(
−
8
)
)
(ii)
(
2
,
(
−
4
)
)
(iii)
(
1
,
(
−
7
)
)
(iv)
(
(
−
1
)
,
(
−
5
)
)
(v)
(
0
,
(
−
6
)
)
Question
6
6.
Find the ratio in which point
(
40
7
,
(
−
38
7
)
)
divides the join of points
(
8
,
(
−
6
)
)
and
(
(
−
8
)
,
(
−
2
)
)
(i)
2
:
6
(ii)
1
:
8
(iii)
0
:
6
(iv)
1
:
6
(v)
1
:
3
Question
7
7.
One end of the diameter of a circle is
(
6
,
(
−
3
)
)
.
If the centre is
(
7
2
,
(
−
1
)
)
,
find the other end of the diameter
(i)
(
(
−
1
)
,
(
−
1
)
)
(ii)
(
0
,
2
)
(iii)
(
2
,
0
)
(iv)
(
1
,
1
)
(v)
(
3
,
3
)
Question
8
8.
Find the coordinates of the points of trisection of the line segment
joining the points
(
(
−
1
)
,
(
−
8
)
)
and
(
(
−
3
)
,
(
−
4
)
)
(i)
(
(
−
2
3
)
,
(
−
23
3
)
)
,
(
(
−
7
3
)
,
(
−
16
3
)
)
(ii)
(
(
−
11
3
)
,
(
−
26
3
)
)
,
(
(
−
7
3
)
,
(
−
16
3
)
)
(iii)
(
(
−
5
3
)
,
(
−
20
3
)
)
,
(
(
−
10
3
)
,
(
−
13
3
)
)
(iv)
(
1
3
,
(
−
14
3
)
)
,
(
(
−
7
3
)
,
(
−
16
3
)
)
(v)
(
(
−
5
3
)
,
(
−
20
3
)
)
,
(
(
−
7
3
)
,
(
−
16
3
)
)
Question
9
9.
In what ratio is the join of
(
4
,
7
)
and
(
(
−
7
)
,
(
−
2
)
)
divided by x-axis?
(i)
7
:
6
(ii)
8
:
2
(iii)
7
:
2
(iv)
6
:
2
(v)
7
:
0
Question
10
10.
In what ratio is the join of
(
8
,
8
)
and
(
(
−
3
)
,
(
−
1
)
)
divided by y-axis?
(i)
3
:
9
(ii)
8
:
0
(iii)
8
:
3
(iv)
1
:
9
(v)
8
:
5
Question
11
11.
Two vertices of a triangle are
(
(
−
2
)
,
0
)
,
(
4
,
5
)
and its centriod is
(
(
−
2
)
,
1
3
)
. Find the coordinates of the third vertex of the triangle
(i)
(
(
−
8
)
,
(
−
4
)
)
(ii)
(
8
,
(
−
4
)
)
(iii)
(
8
,
4
)
(iv)
(
(
−
4
)
,
(
−
8
)
)
(v)
(
(
−
8
)
,
4
)
Question
12
12.
The centre of a circle is
(
2
,
13
2
)
.
Find the other end of the diameter whose one end point is
(
8
,
5
)
(i)
(
(
−
4
)
,
8
)
(ii)
(
(
−
4
)
,
(
−
8
)
)
(iii)
(
8
,
(
−
4
)
)
(iv)
(
4
,
(
−
8
)
)
(v)
(
4
,
8
)
Question
13
13.
The points B
(
0
,
1
)
and D
(
(
−
9
)
,
0
)
are the opposite vertices
of a square ABCD. Find the other two vertices
(i)
(
(
−
4
)
,
(
−
4
)
)
,
(
(
−
6
)
,
6
)
(ii)
(
(
−
4
)
,
(
−
4
)
)
,
(
(
−
5
)
,
5
)
(iii)
(
(
−
3
)
,
(
−
5
)
)
,
(
(
−
5
)
,
5
)
(iv)
(
(
−
2
)
,
(
−
2
)
)
,
(
(
−
5
)
,
5
)
(v)
(
(
−
6
)
,
(
−
6
)
)
,
(
(
−
5
)
,
5
)
Question
14
14.
Find the coordinates of the midpoints of the sides of the quadrilateral
formed by
(
(
−
4
)
,
2
)
,
(
1
,
5
)
,
(
(
−
3
)
,
8
)
and
(
(
−
5
)
,
7
)
(i)
(
1
2
,
11
2
)
,
(
(
−
1
)
,
13
2
)
,
(
(
−
4
)
,
15
2
)
,
(
(
−
9
2
)
,
9
2
)
(ii)
(
(
−
3
2
)
,
7
2
)
,
(
(
−
1
)
,
13
2
)
,
(
(
−
6
)
,
11
2
)
,
(
(
−
9
2
)
,
9
2
)
(iii)
(
(
−
3
2
)
,
7
2
)
,
(
(
−
1
)
,
13
2
)
,
(
(
−
4
)
,
15
2
)
,
(
(
−
9
2
)
,
9
2
)
(iv)
(
(
−
3
2
)
,
7
2
)
,
(
(
−
1
)
,
13
2
)
,
(
(
−
3
)
,
13
2
)
,
(
(
−
9
2
)
,
9
2
)
(v)
(
(
−
3
2
)
,
7
2
)
,
(
(
−
1
)
,
13
2
)
,
(
(
−
4
)
,
15
2
)
,
(
(
−
11
2
)
,
11
2
)
Question
15
15.
Find the lengths of the medians of a triangle whose vertices are
(
1
,
5
)
,
(
7
,
2
)
and
(
3
,
(
−
7
)
)
(i)
17
2
,
√
34
,
1
2
√
445
(ii)
1
2
√
97
,
√
37
,
3
2
√
5
(iii)
3
2
√
5
,
1
2
√
97
,
1
2
√
97
Question
16
16.
In what ratio is the join of
(
8
,
(
−
2
)
)
and
(
(
−
5
)
,
2
)
divided by the line
(
−
y
)
=
0
?
(i)
2
:
-1
(ii)
2
:
5
(iii)
1
:
2
(iv)
2
:
2
(v)
3
:
2
Question
17
17.
In what ratio is the join of
(
(
−
2
)
,
(
−
2
)
)
and
(
9
,
(
−
1
)
)
divided by the line
x
=
0
?
(i)
2
:
7
(ii)
2
:
12
(iii)
3
:
9
(iv)
1
:
9
(v)
2
:
9
Question
18
18.
Three vertices of a parallelogram are
(
(
−
2
)
,
(
−
3
)
)
,
(
5
,
(
−
3
)
)
and
(
8
,
1
)
.
Find the fourth vertex
(i)
(
(
−
1
)
,
(
−
1
)
)
(ii)
(
3
,
3
)
(iii)
(
2
,
0
)
(iv)
(
0
,
2
)
(v)
(
1
,
1
)
Question
19
19.
Find the centre of the circle, the endpoints of whose
diameter are
(
(
−
8
)
,
6
)
and
(
5
,
7
)
(i)
(
(
−
3
2
)
,
(
−
13
2
)
)
(ii)
(
13
2
,
(
−
3
2
)
)
(iii)
(
3
2
,
(
−
13
2
)
)
(iv)
(
(
−
3
2
)
,
13
2
)
(v)
(
3
2
,
13
2
)
Question
20
20.
Determine the ratio in which the line
(
x
−
3
y
+
5
)
=
0
divides the join of points
(
1
,
(
−
1
)
)
and
(
1
,
3
)
(i)
-2
:
1
(ii)
-3
:
1
(iii)
-3
:
4
(iv)
-3
:
-1
(v)
-4
:
1
Question
21
21.
A and B are two points on the x-axis and y-axis respectively.
If
(
3
,
(
−
6
)
)
is the mid-point of the join of A and B, find A and B
(i)
(
7
,
(
−
1
)
)
,
(
0
,
(
−
12
)
)
(ii)
(
6
,
0
)
,
(
0
,
(
−
12
)
)
(iii)
(
8
,
2
)
,
(
0
,
(
−
12
)
)
(iv)
(
4
,
(
−
2
)
)
,
(
0
,
(
−
12
)
)
(v)
(
6
,
0
)
,
(
(
−
1
)
,
(
−
11
)
)
Question
22
22.
If A
(
8
,
4
)
and B
(
(
−
1
)
,
(
−
4
)
)
are two points,
find the coordinates of the point C on AB produced so that AC = 2BC
(i)
(
(
−
8
)
,
(
−
10
)
)
(ii)
(
(
−
12
)
,
(
−
14
)
)
(iii)
(
(
−
11
)
,
(
−
11
)
)
(iv)
(
(
−
10
)
,
(
−
12
)
)
(v)
(
(
−
9
)
,
(
−
13
)
)
Question
23
23.
The mid-point of the join of points
(
4
,
(
−
6
)
)
and
(
(
−
1
)
,
(
−
8
)
)
is
(i)
(
1
2
,
(
−
6
)
)
(ii)
(
5
2
,
(
−
8
)
)
(iii)
(
7
2
,
(
−
5
)
)
(iv)
(
(
−
1
2
)
,
(
−
9
)
)
(v)
(
3
2
,
(
−
7
)
)
Question
24
24.
Find the centroid of the triangle formed by the points
(
5
,
(
−
3
)
)
,
(
5
,
5
)
and
(
(
−
6
)
,
2
)
(i)
(
1
3
,
7
3
)
(ii)
(
(
−
2
3
)
,
(
−
2
3
)
)
(iii)
(
7
3
,
1
3
)
(iv)
(
10
3
,
10
3
)
(v)
(
4
3
,
4
3
)
Question
25
25.
The coordinates of the origin are
(i)
(
1
,
0
)
(ii)
(
0
,
0
)
(iii)
(
1
,
1
)
(iv)
(
0
,
3
)
(v)
(
6
,
0
)
Question
26
26.
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)
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(iii)
(
x
1
−
x
2
2
,
y
1
−
y
2
2
)
(iv)
(
x
1
+
x
2
3
,
y
1
+
y
2
3
)
(v)
(
y
1
−
y
2
2
,
x
1
−
x
2
2
)
Question
27
27.
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
3
,
y
1
−
y
2
−
y
3
3
)
(ii)
(
y
1
+
y
2
+
y
3
2
,
x
1
+
x
2
+
x
3
2
)
(iii)
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
)
(iv)
(
x
1
−
x
2
−
x
3
2
,
y
1
−
y
2
−
y
3
2
)
(v)
(
y
1
−
y
2
−
y
3
2
,
x
1
−
x
2
−
x
3
2
)
Question
28
28.
Find the point that bisects
(
(
−
8
)
,
2
)
and
(
3
,
7
)
(i)
(
(
−
9
2
)
,
5
2
)
(ii)
(
(
−
1
2
)
,
13
2
)
(iii)
(
(
−
7
2
)
,
11
2
)
(iv)
(
(
−
5
2
)
,
9
2
)
(v)
(
(
−
3
2
)
,
7
2
)
Question
29
29.
If point P
(
(
−
7
2
)
,
9
2
)
bisects A
(
(
−
3
)
,
1
)
and B
(
x
,
y
)
, find
(
x
,
y
)
(i)
(
(
−
6
)
,
6
)
(ii)
(
(
−
2
)
,
10
)
(iii)
(
(
−
5
)
,
9
)
(iv)
(
(
−
3
)
,
7
)
(v)
(
(
−
4
)
,
8
)
Question
30
30.
If point P
(x,2)
is equidistant from the points
(
(
−
6
)
,
4
)
and
(
4
,
1
)
, find x
(i)
(
-25
22
)
(ii)
(
-23
20
)
(iii)
(
-21
20
)
(iv)
(
-7
6
)
(v)
(
-5
4
)
Question
31
31.
The line
(
2
y
−
9
)
=
0
bisects which of the following pairs of points?
(i)
(
(
−
4
)
,
3
)
,
(
(
−
5
)
,
5
)
(ii)
(
(
−
5
)
,
4
)
,
(
(
−
6
)
,
6
)
(iii)
(
(
−
7
)
,
2
)
,
(
(
−
5
)
,
5
)
(iv)
(
(
−
5
)
,
4
)
,
(
(
−
5
)
,
5
)
(v)
(
(
−
3
)
,
6
)
,
(
(
−
5
)
,
5
)
Assignment Key
1) (v)
2) (ii)
3) (iii)
4) (ii)
5) (v)
6) (iv)
7) (iv)
8) (v)
9) (iii)
10) (iii)
11) (i)
12) (i)
13) (ii)
14) (iii)
15) (i)
16) (iv)
17) (v)
18) (v)
19) (iv)
20) (ii)
21) (ii)
22) (iv)
23) (v)
24) (v)
25) (ii)
26) (ii)
27) (iii)
28) (iv)
29) (v)
30) (ii)
31) (iv)
