use the distance formula to determine the coordinate of P.

Question

Point P lies on the y-axis. The coordinate of A and B are (-21,0) and (15,0) respectively. If the sum of the distance PA and PB is 54, use the distance formula to determine the coordinate of P.

Answer 1

P to A contains (0, y) and (-21, 0)

P to B contain (0, y) and (15, 0)

 

The distance formula is

 

d = √[(x₁ - x₂)² + (y₁ - y₂)²]

 

 

Plugging in the values,

 

√[(0 - (-21))² + (y - 0)²] + √[(0 - 15)² + (y - 0)²] = 54

 

√(441 + y²) + √(225 + y²) = 54

 

 

Square both sides of the equation.

 

(441 + y²) + 2√((441 + y²)(225 + y²)) + (225 + y²) = 2916

 

2y² + 666 + 2√((441 + y²)(225 + y²)) = 2916

 

2√((441 + y²)(225 + y²)) = -2y² + 2250

 

 

Square both sides of the equation again to undo the radical.  Then after you do that, manipulate the equation to get a quadratic equation.  From there, you can solve for y.