Question

if a (1, 2) and b(3,8) are two given points then the point P such that PA is equal to PB and area of triangle PAB is equal to 10 is​

Answer 1

Given: A and b are two points (3,4) , (5,-2) and PA=PB and area of triangle PAB= 10 square units.

To find: The coordinates of P

Solution: Let the coordinate P be (x,y)

Since it is given that PA = PB

So, firstly we will calculate the distance PA.

PA = (x,y) (3,4)

Distance PA =

PB=(x,y) (5,-2)

Distance PB =

So,

Squaring both the sides in the above equation,

  (Equation 1)

Now,it is given that Area of triangle PAB = 10

Area of triangle of (3,4) (5,-2) and (x,y)

Area of triangle is given by the formula=

Area of triangle PAB =

          (Equation 2)

Now, solving equations 1 and 2.

Since

therefore, x = 3y+1

Equation 2 implies,

Therefore, the coordinates are (7,2).

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