Answer:
p = ± 5[tex]\sqrt{2}[/tex]
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 = [tex]\sqrt{(0-p)^2+(p-0)^2}[/tex]
= [tex]\sqrt{(-p)^2+p^2}[/tex]
= [tex]\sqrt{p^2+p^2}[/tex]
= [tex]\sqrt{2p^2}[/tex]
Given that d = 10, then
[tex]\sqrt{2p^2}[/tex] = 10 ( square both sides )
([tex]\sqrt{2p^2}[/tex] )² = 10², that is
2p² = 100 ( divide both sides by 2 )
p² = 50 ( take the square root of both sides )
p = ± [tex]\sqrt{50}[/tex] = ± [tex]\sqrt{25(2)}[/tex] = ± 5[tex]\sqrt{2}[/tex]
The possible value of p is equal to 7.1 units.
Data;
The distance between two points can be calculated using the formula
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2} \\[/tex]
Let's substitute the values into the equation;
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2} \\10 = \sqrt{(p-0)^2 - (p-0)^2} \\10 = \sqrt{p^2 + p^2}\\\\10 = \sqrt{2p^2}[/tex]
Let's take the squares of both sides
[tex]10 = \sqrt{2p^2} \\(10)^2 = (\sqrt{2p^2})^2\\ 100 = 2p^2\\p^2 = 50\\p = \sqrt{50}\\ p = 7.07\\p = 7.1[/tex]
The possible value of p is equal to 7.1 units.
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