Q29 of 47 Page 1

If the coordinates of two points are A(3, 4), B(5, –2), and a point P (x, 5) is such that PA = PB then find the area of ∆PAB.

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

Using Section formula:


M(x, y) =


⇒ M(x, y) = (4 , 1)


Slope of line AB(m1) =


⇒ m1 = -3


From the perpendicularity relationship we know m1 × m2 = -1


Slope of line PM(m2) = …Equation(i)


Slope of line PM(m2) 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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