Answer:
see explanation
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (1, a)
d = [tex]\sqrt{(1-3)^2+(a-5)^2}[/tex]
= [tex]\sqrt{(-2)^2+(a-5)^2}[/tex]
= [tex]\sqrt{4+(a-5)^2}[/tex]
Equating d to [tex]\sqrt{8}[/tex], gives
[tex]\sqrt{4+(a-5)^2}[/tex] = [tex]\sqrt{8}[/tex]
Squaring both sides
4 + (a - 5)² = 8 ( subtract 4 from both sides )
(a - 5)² = 4 ( take the square root of both sides )
a - 5 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 5 to both sides )
a = 5 ± 2, that is
a = 5 - 2 = 3 OR a = 5 + 2 = 7
