Answer:
y = - 5 or y = 9
Step-by-step explanation:
using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (- 1, y )
d = [tex]\sqrt{(-1-4)^2+(y-2)^2}[/tex]
= [tex]\sqrt{(-5)^2+(y-2)^2}[/tex]
= [tex]\sqrt{25+(y-2)^2}[/tex]
equating to [tex]\sqrt{74}[/tex] , that is
[tex]\sqrt{25+(y-2)^2}[/tex] = [tex]\sqrt{74}[/tex] ( square both sides )
25 + (y - 2)² = 74 ( subtract 25 from both sides )
(y - 2)² = 49 ( take square root of both sides )
y - 2 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 2 to both sides )
y = 2 ± 7
Then
y = 2 + 7 = 9 or y = 2 - 7 = - 5
