Question

Let A=(0,0) and B=(12,5). Find points on the y-axis that are twice as far from B as from A. Solve algebraically.

Answer 1

ok, this problem and needs the distance formula

call the point on the y axis P(0, y)

then you have 2AP = BP

\[2\sqrt{(0 - 0)^2 + (y - 0)^2} = \sqrt{(0 - 12)^2 + ( y - 5)^2}\]

square both sides

\[4y^2 = 144 + (y - 5)^2\]

you need to now solve for y

Answer 2

the solution will need the general quadratic formula.

Answer 3

Thank you!