Question

if the distance of (p,4) from the point (5,0) is 5 find p​

Answer 1

Answer:

p = 8 or 2

Explanation:

x1 = p, x2 = 5, y1 = 4, y2 = 0

distance =$\sqrt{(x_{1}-x_{2})^2 + (y_{1} -y_{2})^2 }$ =  $\sqrt{(p-5)^2 + (4-0)^2 }$ =

              =$\sqrt{(p-5)^2 + 4^2} = \sqrt{p^2 - 10p +25+16}$ = 5

square on both sides,

p² - 10p +41 = 25

p² - 10p + 16 = 0

this is in the form of a quadratic equation

so, p = (-b±√(b²-4ac)) / 2a

     p = 10±√100 - 64 / 2 = 10±√36 / 2 = 10±6 / 2

     p = 8  or  2