EduSahara™ Assignment
Name : Geometric Figure Properties and Collinearity
Chapter : Coordinate Geometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The points
(
(
−
5
)
,
1
)
,
(
(
−
5
)
,
(
−
6
)
)
and
(
(
7
2
√
3
−
5
)
,
(
−
5
2
)
)
represent
(i)
right angled triangle
(ii)
scalene triangle
(iii)
equilateral triangle
(iv)
isosceles triangle
Question
2
2.
The points
(
(
−
6
)
,
2
)
,
(
(
−
5
)
,
(
−
6
)
)
and
(
3
2
,
(
−
9
8
)
)
represent
(i)
equilateral triangle
(ii)
collinear points
(iii)
isosceles triangle
(iv)
right angle triangle
(v)
scalene triangle
Question
3
3.
The points
(
(
−
5
)
,
(
−
2
)
)
,
(
(
−
1
)
,
2
)
,
(
3
,
(
−
2
)
)
and
(
(
−
1
)
,
(
−
6
)
)
represent
(i)
parallelogram
(ii)
square
(iii)
rhombus
(iv)
rectangle
(v)
trapezium
Question
4
4.
The points
(
(
−
5
)
,
(
−
4
)
)
,
(
2
,
(
−
4
)
)
,
(
6
,
(
−
1
)
)
and
(
(
−
1
)
,
(
−
1
)
)
represent
(i)
square
(ii)
rectangle
(iii)
parallelogram
(iv)
trapezium
(v)
rhombus
Question
5
5.
The points
(
(
−
6
)
,
(
−
2
)
)
,
(
2
,
(
−
2
)
)
,
(
2
,
2
)
and
(
(
−
6
)
,
2
)
represents
(i)
rhombus
(ii)
square
(iii)
parallelogram
(iv)
trapezium
(v)
rectangle
Question
6
6.
The points
(
(
−
8
)
,
3
)
,
(
1
,
(
−
7
)
)
and
(
(
−
2
)
,
5
)
represent
(i)
equilateral triangle
(ii)
scalene triangle
(iii)
collinear points
(iv)
isosceles triangle
(v)
right angle triangle
Question
7
7.
The points
(
(
−
6
)
,
(
−
1
)
)
,
(
(
−
3
)
,
2
)
and
(
0
,
(
−
1
)
)
represent
(i)
isosceles right angled triangle
(ii)
equilateral triangle
(iii)
right angle triangle
(iv)
collinear points
(v)
scalene triangle
Question
8
8.
The points
(
(
−
2
)
,
(
−
1
)
)
,
(
4
,
(
−
1
)
)
and
(
4
,
2
)
represent
(i)
collinear points
(ii)
isosceles right angled triangle
(iii)
scalene triangle
(iv)
equilateral triangle
(v)
right angle triangle
Question
9
9.
The points
(
(
−
4
)
,
(
−
2
)
)
,
(
3
,
(
−
6
)
)
,
(
10
,
(
−
2
)
)
and
(
3
,
2
)
represent
(i)
square
(ii)
rhombus
(iii)
rectangle
(iv)
parallelogram
(v)
trapezium
Question
10
10.
The points
(
6
,
3
)
,
(
(
−
6
)
,
(
−
3
)
)
and
(
(
−
18
13
)
,
(
−
9
13
)
)
represents
(i)
right angle triangle
(ii)
collinear points
(iii)
equilateral triangle
(iv)
isoceles triangle
Question
11
11.
Find the value of k such that the points
(
(
−
7
)
,
(
−
7
)
)
,
(
(
−
112
15
)
,
0
)
and
(k,8)
are collinear
(i)
-9
(ii)
-8
(iii)
-10
(iv)
-7
(v)
-5
Question
12
12.
Find the value of k such that the points
(
(
−
6
)
,
(
−
2
)
)
,
(
(
−
76
11
)
,
3
)
and
(-8,k)
are collinear
(i)
9
(ii)
7
(iii)
10
(iv)
8
(v)
12
Question
13
13.
Which of the following sets of points are collinear?
(i)
(
(
−
1
)
,
0
)
,
(
(
−
2
)
,
8
)
,
(
(
−
3
)
,
7
)
(ii)
(
(
−
4
)
,
(
−
7
)
)
,
(
7
,
7
)
,
(
1
,
(
−
4
)
)
(iii)
(
(
−
7
)
,
5
)
,
(
(
−
8
)
,
(
−
7
)
)
,
(
(
−
25
4
)
,
14
)
(iv)
(
(
−
3
)
,
0
)
,
(
5
,
5
)
,
(
5
,
(
−
7
)
)
(v)
(
(
−
4
)
,
3
)
,
(
3
,
(
−
1
)
)
,
(
6
,
(
−
4
)
)
Question
14
14.
Find the area of the quadrilateral formed by
(
(
−
5
)
,
5
)
,
(
1
,
8
)
,
(
(
−
4
)
,
12
)
and
(
(
−
6
)
,
9
)
(i)
26
(ii)
25
(iii)
22
(iv)
24
(v)
28
Question
15
15.
Find the relation between x and y if the points
(
x
,
y
)
,
(
(
−
1
)
,
6
)
and
(
(
−
5
)
,
(
−
6
)
)
are collinear
(i)
(
9
x
−
6
y
+
9
)
=
0
(ii)
(
9
x
−
y
+
39
)
=
0
(iii)
(
−
5
y
+
15
)
=
0
(iv)
(
−
12
x
+
4
y
−
36
)
=
0
(v)
(
−
3
x
+
3
y
−
21
)
=
0
Question
16
16.
Find the area of the triangle
formed by the points
(
0
,
(
−
1
)
)
,
(
(
−
5
)
,
(
−
4
)
)
and
(
7
,
4
)
(i)
3
(ii)
0
(iii)
4
(iv)
2
(v)
1
Question
17
17.
Find the perimeter of the triangle formed by the points
(
3
,
(
−
4
)
)
,
(
2
,
7
)
and
(
0
,
4
)
(i)
(
√
122
+
√
11
+
√
73
)
(ii)
(
√
122
+
√
13
+
73
)
(iii)
(
√
122
+
√
13
+
4
√
73
)
(iv)
(
√
122
+
√
15
+
√
73
)
(v)
(
√
122
+
√
13
+
√
73
)
Question
18
18.
Find the lengths of the sides of the triangle formed by the points
(
8
,
7
)
,
(
(
−
4
)
,
0
)
and
(
(
−
8
)
,
4
)
(i)
4
√
193
,
4
√
2
,
√
265
(ii)
√
193
,
4
√
2
,
√
265
(iii)
√
193
,
4
√
2
,
√
268
(iv)
√
193
,
8
,
√
265
Assignment Key
1) (iii)
2) (iii)
3) (ii)
4) (iii)
5) (v)
6) (ii)
7) (i)
8) (v)
9) (ii)
10) (ii)
11) (ii)
12) (i)
13) (iii)
14) (ii)
15) (iv)
16) (iv)
17) (v)
18) (ii)
