Answer:
A (0, - 2 ) or A (0, 6 )
Step-by-step explanation:
Using the distance formula
d = [tex]\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2 }[/tex]
with (x₁, y₁ ) = B(3, 2) and (x₂, y₂ ) = A(0, y )
AB = [tex]\sqrt{(0-3)^2+(y-2)^2}[/tex]
= [tex]\sqrt{(-3)^2+(y-2)^2}[/tex]
= [tex]\sqrt{9+(y-2)^2}[/tex]
Given AB = 5 then equating gives
[tex]\sqrt{9+(y-2)^2}[/tex] = 5 ( square both sides )
9 + (y - 2)² = 25 ( subtract 9 from both sides )
(y - 2)² = 16 ( take square root of both sides )
y - 2 = ± [tex]\sqrt{16}[/tex] = ± 4 ( add 2 to both sides )
y = 2 ± 4
Then y = 2 - 4 = - 2 or y = 2 + 4 = 6
Possible coordinates of point A are
A (0, - 2 ) or A (0, 6 )
