Answer :

Answer:

a = - 5 or 1

Step-by-step explanation:

given the points (a, 10 ) and (- 2, 6 ) are 5 units apart

Using the distance formula

• d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

let (x₁, y₁ ) = (- 2, 6 ) , (x₂, y₂ ) = (a, 10 ) and d = 5

substitute these values into the formula for d

[tex]\sqrt{(a-(-2))^2+(10-6)^2}[/tex] = 5

[tex]\sqrt{(a+2)^2+4^2}[/tex] = 5 ( square both sides )

(a + 2)² + 16 = 25 ( subtract 16 from both sides )

(a + 2)² = 9 ( take square root of both sides )

[tex]\sqrt{(a+2)^2}[/tex] = ± [tex]\sqrt{9}[/tex]

a + 2 = ± 3 ( subtract 2 from both sides )

a = - 2 ± 3

Then

a = - 2 - 3 = - 5

or

a = - 2 + 3 = 1

Thus a = - 5 or a = 1