Question

If the distance between the points A(p,0) and B(p,0) is 10, find the possible values of p

Answer 1

Answer:

p = ± 5$\sqrt{2}$

Step-by-step explanation:

Calculate the distance using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (p, 0) and (x₂, y₂ ) = (0, p)

d = $\sqrt{(0-p)^2+(p-0)^2}$

   = $\sqrt{(-p)^2+p^2}$

   = $\sqrt{p^2+p^2}$

   = $\sqrt{2p^2}$

Given that d = 10, then

$\sqrt{2p^2}$ = 10 ( square both sides )

($\sqrt{2p^2}$ )² = 10², that is

2p² = 100 ( divide both sides by 2 )

p² = 50 ( take the square root of both sides )

p = ± $\sqrt{50}$ = ± $\sqrt{25(2)}$ = ± 5$\sqrt{2}$