EduSahara™ Assignment
Name : Coordinate Geometry Miscellaneous
Chapter : Coordinate Geometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Find the area of the triangle
formed by the points
(
1
,
(
−
6
)
)
,
(
1
,
(
−
7
)
)
and
(
(
−
6
)
,
(
−
5
)
)
(i)
5
2
(ii)
7
2
(iii)
13
4
(iv)
4
(v)
9
2
Question
2
2.
Find the perimeter of the triangle formed by the points
(
7
,
(
−
7
)
)
,
(
(
−
5
)
,
3
)
and
(
6
,
1
)
(i)
(
2
√
61
+
5
√
5
+
√
65
)
(ii)
(
2
√
61
+
5
√
7
+
√
65
)
(iii)
(
2
√
61
+
5
√
5
+
65
)
(iv)
(
2
√
61
+
5
√
3
+
√
65
)
(v)
(
2
√
61
+
5
√
5
+
4
√
65
)
Question
3
3.
The points
(
(
−
1
)
,
(
−
5
)
)
,
(
1
,
6
)
and
(
(
−
11
2
√
3
)
,
(
1
2
+
√
3
)
)
represent
(i)
equilateral triangle
(ii)
scalene triangle
(iii)
isosceles triangle
(iv)
right angled triangle
Question
4
4.
The points
(
(
−
6
)
,
(
−
1
)
)
,
(
(
−
2
)
,
(
−
6
)
)
and
(
(
−
49
6
)
,
(
−
41
6
)
)
represent
(i)
equilateral triangle
(ii)
scalene triangle
(iii)
right angle triangle
(iv)
isosceles triangle
(v)
collinear points
Question
5
5.
The points
(
(
−
5
)
,
(
−
2
)
)
,
(
(
−
2
)
,
1
)
,
(
1
,
(
−
2
)
)
and
(
(
−
2
)
,
(
−
5
)
)
represent
(i)
square
(ii)
trapezium
(iii)
rectangle
(iv)
parallelogram
(v)
rhombus
Question
6
6.
The points
(
(
−
3
)
,
(
−
5
)
)
,
(
3
,
(
−
5
)
)
,
(
6
,
(
−
1
)
)
and
(
0
,
(
−
1
)
)
represent
(i)
parallelogram
(ii)
trapezium
(iii)
square
(iv)
rectangle
(v)
rhombus
Question
7
7.
The points
(
(
−
5
)
,
(
−
1
)
)
,
(
1
,
(
−
1
)
)
,
(
1
,
4
)
and
(
(
−
5
)
,
4
)
represents
(i)
trapezium
(ii)
rhombus
(iii)
rectangle
(iv)
square
(v)
parallelogram
Question
8
8.
The points
(
3
,
(
−
8
)
)
,
(
2
,
4
)
and
(
4
,
1
)
represent
(i)
equilateral triangle
(ii)
scalene triangle
(iii)
isosceles triangle
(iv)
right angle triangle
(v)
collinear points
Question
9
9.
The points
(
(
−
3
)
,
(
−
4
)
)
,
(
0
,
(
−
1
)
)
and
(
3
,
(
−
4
)
)
represent
(i)
collinear points
(ii)
right angle triangle
(iii)
scalene triangle
(iv)
equilateral triangle
(v)
isosceles right angled triangle
Question
10
10.
The points
(
(
−
4
)
,
(
−
4
)
)
,
(
4
,
(
−
4
)
)
and
(
4
,
(
−
1
)
)
represent
(i)
scalene triangle
(ii)
equilateral triangle
(iii)
collinear points
(iv)
isosceles right angled triangle
(v)
right angle triangle
Question
11
11.
The points
(
(
−
4
)
,
(
−
5
)
)
,
(
3
,
(
−
10
)
)
,
(
10
,
(
−
5
)
)
and
(
3
,
0
)
represent
(i)
rhombus
(ii)
rectangle
(iii)
parallelogram
(iv)
square
(v)
trapezium
Question
12
12.
The points
(
6
,
(
−
7
)
)
,
(
(
−
6
)
,
7
)
and
(
(
−
8
3
)
,
28
9
)
represents
(i)
collinear points
(ii)
equilateral triangle
(iii)
right angle triangle
(iv)
isoceles triangle
Question
13
13.
Find the value of k such that the points
(
(
−
9
)
,
8
)
,
(
(
−
5
)
,
68
9
)
and
(k,7)
are collinear
(i)
1
(ii)
-1
(iii)
0
(iv)
-3
(v)
3
Question
14
14.
Find the value of k such that the points
(
(
−
5
)
,
(
−
7
)
)
,
(
(
−
23
7
)
,
(
−
10
7
)
)
and
(-1,k)
are collinear
(i)
7
(ii)
5
(iii)
4
(iv)
6
(v)
9
Question
15
15.
Which of the following sets of points are collinear?
(i)
(
(
−
7
)
,
(
−
6
)
)
,
(
5
,
(
−
2
)
)
,
(
7
,
1
)
(ii)
(
7
,
6
)
,
(
0
,
6
)
,
(
3
,
(
−
5
)
)
(iii)
(
(
−
6
)
,
(
−
7
)
)
,
(
0
,
(
−
6
)
)
,
(
2
,
(
−
8
)
)
(iv)
(
3
,
(
−
4
)
)
,
(
0
,
(
−
5
)
)
,
(
3
,
(
−
8
)
)
(v)
(
(
−
7
)
,
(
−
8
)
)
,
(
3
,
(
−
8
)
)
,
(
(
−
4
)
,
(
−
8
)
)
Question
16
16.
(
(
−
7
)
,
8
)
,
(
0
,
1
)
and
(
5
,
2
)
are the vertices of triangle ABC.
Find the equation of the median of the triangle through vertex C
(i)
(
13
2
x
+
19
2
y
−
61
2
)
=
0
(ii)
(
−
4
x
−
y
+
1
)
=
0
(iii)
(
−
5
2
x
−
19
2
y
+
59
2
)
=
0
(iv)
(
−
5
2
x
−
15
2
y
+
59
2
)
=
0
(v)
(
−
5
2
x
−
17
2
y
+
59
2
)
=
0
Question
17
17.
Find the area of the quadrilateral formed by
(
(
−
4
)
,
2
)
,
(
2
,
5
)
,
(
(
−
1
)
,
8
)
and
(
(
−
4
)
,
8
)
(i)
45
(ii)
43
2
(iii)
45
4
(iv)
45
2
(v)
47
2
Question
18
18.
Find the relation between x and y such that the point P
(
x
,
y
)
is equidistant from points
(
0
,
(
−
7
)
)
and
(
(
−
7
)
,
(
−
1
)
)
(i)
(
2
x
−
3
y
−
21
)
=
0
(ii)
(
−
14
x
+
12
y
−
1
)
=
0
(iii)
(
−
14
x
+
15
y
−
1
)
=
0
(iv)
(
−
15
x
+
12
y
−
1
)
=
0
(v)
(
2
x
−
6
y
−
21
)
=
0
Question
19
19.
Find the relation between x and y if the points
(
x
,
y
)
,
(
(
−
4
)
,
(
−
3
)
)
and
(
(
−
5
)
,
(
−
4
)
)
are collinear
(i)
(
−
4
x
−
11
y
−
64
)
=
0
(ii)
(
−
x
+
y
−
1
)
=
0
(iii)
(
−
7
x
−
9
y
−
30
)
=
0
(iv)
(
3
x
−
2
y
+
7
)
=
0
(v)
(
2
x
−
y
+
5
)
=
0
Assignment Key
1) (ii)
2) (i)
3) (i)
4) (iv)
5) (i)
6) (i)
7) (iii)
8) (ii)
9) (v)
10) (v)
11) (i)
12) (i)
13) (iii)
14) (iv)
15) (v)
16) (v)
17) (iv)
18) (ii)
19) (ii)
