Solve
Study
Textbooks
Guides
Use app
Login
Question
Let
A
(
0
,
−
6
)
,
B
(
1
,
2
)
,
C
(
3
,
−
3
)
,
D
(
−
3
,
2
)
,
and
E
(
−
4
,
−
2
)
be given points, then which of the following is (are) true?
A
Area of pentagon formed by these points is
2
7
3
B
Area of triangle formed by points below x-axis is 12 square units
C
Angle subtended by
B
D
at
A
is
tan
−
1
6
1
3
2
D
All of these
Medium
Open in App
Solution
Verified by Toppr
Correct option is D)
Given the points
A(0,-6), B(1,2), C(3,-3),D(-3,2) and E(-4,-2)
Area of the pentagon = Area formed by a polygon =
∣
∣
∣
∣
∣
2
(
x
1
y
2
−
y
1
x
2
)
+
(
x
2
y
3
−
y
2
x
3
)
.
.
.
+
(
x
n
y
1
−
y
n
x
1
)
∣
∣
∣
∣
∣
where
a
1
is the coordinate of vertex 1 and
y
n
is the y-coordinate of the nth vertex etc.
Area
∣
∣
∣
∣
∣
2
[
(
−
3
×
2
)
−
(
2
×
1
)
]
+
[
(
1
×
−
3
)
−
(
3
×
2
)
]
+
[
(
3
×
−
6
)
−
(
−
3
×
0
)
]
+
[
(
−
4
×
−
2
)
−
(
−
2
×
−
3
)
]
+
[
(
0
×
−
2
)
−
(
−
6
×
−
4
)
]
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
−
2
7
3
∣
∣
∣
∣
∣
=
2
7
3
Area of triangle formed by points below $$x-axis,
Area
=
2
1
b
h
=
×
−
6
=
2
2
4
=
1
2
square unit
Angle subtended by BD at
A
=
tan
−
1
(
6
1
8
2
)
Was this answer helpful?
0
0
Similar questions
Then which of the following is true?
Medium
View solution
>
ABCD is a quadrilateral. Then which of the following is true?
Easy
View solution
>
Which of the following is true?
Medium
View solution
>
Let ABCD be a parallelogram. Let AP, CQ be the
⊥
from A and C on its diagonal BD. Which of the following is true.
This question has multiple correct options
Medium
View solution
>
For a triangle ABC, which of the following is true?
Easy
View solution
>