Answer :
Answer:
(a) If A is the origin, then the cordinates are: P = (4, 6), Q = (3, 2), R (6, 5) respectively.
(b) The coordinates of vertices of the triangle PQR, if C is the origin: P = (-12, -2), Q = (-13, -6), R = (-10, -3)
(c) Area of triangle PQR in case of origin A:
=
1
2
[
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
]
=
1
2
[
4
(
2
−
5
)
+
3
(
5
−
6
)
+
6
(
6
−
2
)
]
=
1
2
(
−
12
−
3
+
24
)
=
9
2
s
q
u
n
i
t
Area of triangle PQR in case of origin C:
=
1
2
[
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
]
=
1
2
[
−
12
(
−
6
+
3
)
+
−
13
(
−
3
+
2
)
+
(
−
10
)
(
−
2
+
6
)
]
=
1
2
(
36
+
13
−
40
)
=
9
2
s
q
u
n
i
t
Area is same in both the cases because triangle remains the same no matter which point is considered as origin.