Answer :

Let the midpoint of AB be M(x, y)

Using Section formula:

M(x, y) =

⇒ M(x, y) = (4 , 1)

Slope of line AB(m_{1}) =

⇒ m_{1} = -3

From the perpendicularity relationship we know m_{1} × m_{2} = -1

Slope of line PM(m_{2}) = …Equation(i)

Slope of line PM(m_{2}) from Two-point formula = …Equation(ii)

Equating equation (i) & (ii)

⇒ 12 = 4-x

⇒ x = -8

P(-8, 5)

Length AB =

Length AB = 2√10 units

Length PM =

Length PM = 4√10 units

Area of ∆PAB = 0.5 × 2√10 × 4√10

**Answer:** Area of the triangle is 40 sq. units

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