Question

I don't know why the answer can be 3 OR 7. Please help me.

Answer 1

see explanation

Explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (1, a)

d =
`√((1-3)^2+(a-5)^2)`

=
`√((-2)^2+(a-5)^2)`

=
`√(4+(a-5)^2)`

Equating d to
`√(8)`, gives

`√(4+(a-5)^2)` =
`√(8)`

Squaring both sides

4 + (a - 5)² = 8 ( subtract 4 from both sides )

(a - 5)² = 4 ( take the square root of both sides )

a - 5 = ±
`√(4)` = ± 2 ( add 5 to both sides )

a = 5 ± 2, that is

a = 5 - 2 = 3 OR a = 5 + 2 = 7