12. A(5,3), B(3, -2) are two points. If a point P forms a triangle of area 9 square units with
A, B then find the locus of P.
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2
Answer:
Let P(h,k)
Ar△PAB=
2
1
∣
∣
∣
∣
∣
∣
∣
∣
x
1
x
2
x
3
y
1
y
2
y
3
1
1
1
∣
∣
∣
∣
∣
∣
∣
∣
=9
P≡(h,k)≡(x
1
,y
1
)
A≡(5,3)≡(x
2
,y
2
)
B≡(3,−2)≡(x
3
,y
3
)
∴Ar△PAB=
2
1
∣
∣
∣
∣
∣
∣
∣
∣
h
5
3
k
3
−2
1
1
1
∣
∣
∣
∣
∣
∣
∣
∣
=9
upon simplification we get,
5h−2k=37
⇒5x−2y=37 is the required equation.
Explanation:
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