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

Answer:

B

Step-by-step 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 = $\sqrt{(x-1)^2+(-2-6)^2}$

   = $\sqrt{(x-1)^2+(-8)^2}$

   = $\sqrt{(x-1)^2+64}$

given AB = 10, then equating gives

$\sqrt{(x-1)^2+64}$ = 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 = ± $\sqrt{36}$ = ± 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