2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Dot Product
Find the area...
Question
Find the areas of the triangles the coordinates of whose angular points are
(
−
a
,
π
6
)
,
(
a
,
π
2
)
, and
(
−
2
a
,
−
2
π
2
)
Open in App
Solution
Given polar co-ordinates
(
i
)
(
−
a
,
π
6
)
Then,
r
=
−
a
and
θ
=
π
6
x
=
r
cos
θ
=
−
a
×
cos
(
π
6
)
=
−
√
3
a
2
y
=
r
sin
θ
=
−
a
×
sin
(
π
6
)
=
−
a
2
A
(
−
√
3
a
2
,
−
a
2
)
(
i
i
)
(
−
2
a
,
−
π
)
Then,
r
=
−
2
a
and
θ
=
−
π
x
=
r
cos
θ
=
−
2
a
×
cos
(
−
π
)
=
2
a
y
=
r
sin
θ
=
−
2
a
×
sin
(
−
π
)
=
0
B
(
2
a
,
0
)
(
i
i
i
)
(
a
,
π
2
)
Then,
r
=
a
and
θ
=
π
2
x
=
r
cos
θ
=
a
×
cos
(
π
2
)
=
0
y
=
r
sin
θ
=
a
×
sin
(
π
2
)
=
a
C
(
0
,
a
)
Now we have points
A
(
−
√
3
a
2
,
−
a
2
)
,
B
(
2
a
,
0
)
and
C
(
0
,
a
)
Area of triangle having angular points
(
x
1
,
y
1
)
(
x
2
,
y
2
)
(
x
3
,
y
3
)
is given by the formula
△
=
1
2
|
x
1
y
2
+
x
2
y
3
+
x
3
y
1
−
x
2
y
1
−
x
3
y
2
−
x
1
y
3
|
Then,
A
(
△
A
B
C
)
=
1
2
∣
∣
∣
0
+
2
a
2
+
0
−
(
−
a
2
)
−
0
+
√
3
a
2
2
∣
∣
∣
⇒
A
(
△
A
B
C
)
=
a
2
(
6
+
√
3
4
)
Suggest Corrections
0
Similar questions
Q.
Find the areas of the triangles the whose coordinates of the points are respectively.
(0, 4), (3, 6) and ( - 8, - 2)
Q.
Find the length of the straight line joining the pairs of points whose polar coordinates are
(
a
,
π
2
)
and
(
3
a
,
π
6
)
Q.
The area of the triangle whose vertices are
(
a
,
θ
)
,
(
2
a
,
θ
−
π
3
)
and
(
3
a
,
θ
+
2
π
3
)
is
Q.
Lay down the positions of the points whose polar coordinates are
(
2
a
,
−
π
2
)
Q.
Find the area of the triangle formed by the points with polar coordinates
(
1
,
π
6
)
,
(
2
,
π
3
)
,
(
3
,
π
2
)
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
MATHEMATICS
Watch in App
Explore more
Dot Product
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app