Respuesta :
Answer:
a = - 1
Step-by-step explanation:
Given the points are equidistant from A then AP = AQ
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = P(3, - 3)
AP = [tex]\sqrt{3-0)^2+(-3-a)^2}[/tex] = [tex]\sqrt{3^2+(-3-a)^2}[/tex] = [tex]\sqrt{9+(-3-a)^2}[/tex]
Repeat with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = Q(- 2, 2)
AQ = [tex]\sqrt{(-2-0)^2+(2-a)^2}[/tex] = [tex]\sqrt{(-2)^2+(2-a)^2}[/tex] = [tex]\sqrt{4+(2-a)^2}[/tex]
Equating AP and AQ
[tex]\sqrt{9+(-3-a)^2}[/tex] = [tex]\sqrt{4+(2-a)^2}[/tex] ( square both sides )
9 + (- 3 - a)² = 4 + (2 - a )² ← expand parenthesis on both sides
9 + 9 + 6a + a² = 4 + 4 - 4a + a² ( subtract a² - 4a from both sides )
18 + 10a = 8 ( subtract 18 from both sides )
10a = - 10 ( divide both sides by 10 )
a = - 1
