The area of the triangle whose vertices are P(2,-6), Q(5,4) and R(-2,4) is
Answers
Answered by
0
Answer:
6-
Step-by-step explanation:
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Answered by
10
Answer:
Step-by-step explanation:
Using integration finding area of triangle P(2,5)Q(4,7) and R(6,2)
Equation of line PQ
(y−5)=
4−2
7−5
(x−2)⇒y=x+3
Equation of line QR
(y−7)=
6−4
2−7
(x−4)⇒y=
2
−5
x+17
Equation of line PR
(y−5)=
6−2
2−5
(x−2)⇒y=
4
−3
x+
2
13
Area of △PQR
=(area under PQ)+(area under QR)−(area under PR)
=∫
2
4
(x+3)dx+∫
4
6
(−
2
5x
+17)dx−∫
2
6
(
4
−3
x+
2
13
)dx
=[
2
x
2
+3x]
2
4
+[
4
−5x
2
+17x]
4
6
−[
8
3x
2
+
2
13x
]
2
6
=6+3(4−2)+
4
−5
(36−16)+17(6−4)−
8
3
×32−
2
13
×4
=6+6−
4
5
×20+34−12−26
=12−25+34−14=7 sq.unit
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