Question

1 point If the distance from A(1, 6) to B(x, -2) is 10, then what is a possible value for x? (A) 11 (B) -5 (C) -7 (D) 8 (E) 6​

Answer 1

B

Explanation:

calculate the distance between A and B using the distance formula

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

with (x₁, y₁ ) = A (1, 6 ) and (x₂, y₂ ) = B (x, - 2 )

d =
`√((x-1)^2+(-2-6)^2)`

=
`√((x-1)^2+(-8)^2)`

=
`√((x-1)^2+64)`

given AB = 10, then equating gives

`√((x-1)^2+64)` = 10 ( square both sides to clear the radical )

(x - 1)² + 64 = 10² = 100 ( subtract 64 from both sides )

(x - 1)² = 36 ← take square root of both sides

x - 1 = ±
`√(36)` = ± 6 ( add 1 to both sides )

x = 1 ± 6

then

x = 1 - 6 = - 5

x = 1 + 6 = 7

from the list then x = - 5 is a possible value