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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