Question

Find x if the distance between the points (x,6) and (0,21) is d=17. Assume that x≥0.

Answer 1

x = 8

Explanation:

calculate the distance d between the points using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

let (x₁, y₁ ) = (x, 6 ) and (x₂, y₂ ) = (0, 21 )

substitute these values into the formula for d

d =
`√((0-x)^2+(21-6)^2)`

=
`√((-x)^2+15^2)`

=
`√(x^2+225)`

given d = 17 , then equate both

(
`√(x^2+225)` )² = 17

x² + 225 = 289 ( subtract 225 from both sides )

x² = 64 ( take square root of both sides )

`√(x^2)` = ±
`√(64)`

x = ± 8

since x ≥ 0 , then x = 8