Answer:
x = - 2 , x = 4
Step-by-step explanation:
Calculate the distance PQ using the distance formula and equate to 5
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = P (1, 3) and (x₂, y₂ ) = Q (x, 7 )
PQ = [tex]\sqrt{(x-1)^2+(7-3)^2}[/tex] = [tex]\sqrt{(x-1)^2+4^2}[/tex] = [tex]\sqrt{(x-1)^2+16}[/tex] , then
[tex]\sqrt{(x-1)^2+16}[/tex] = 5 ( square both sides )
(x - 1)² + 16 = 25 ( subtract 16 from both sides )
(x - 1)² = 9 ( take square root of both sides )
x - 1 = ± [tex]\sqrt{9}[/tex] = ± 3 ( add 1 to both sides )
x = 1 ± 3
Then
x = 1 - 3 = - 2 , or
x = 1 + 3 = 4
