Question

Point B has coordinates ?(1?,2?). The? x-coordinate of point A is negative 5. The distance between point A and point B is 10 units. What are the possible coordinates of point? A?

Answer 1

(- 5, - 6 ) or (- 5, 10 )

using the distance formula

d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (- 5, y )

d = √(- 5 - 1 )² + (y - 2 )² = 10

d = √36 + (y - 2 )² = 10

square both sides

36 + (y - 2 )² = 100 ( subtract 36 from both sides )

(y - 2 )² = 64

take the square root of both sides

y - 2 = ± 8 ( add 2 to both sides )

y = 2 ± 8

y = 2 + 8 or y = 2 - 8 ⇒ y = 10 or y = - 6

coordinates of A = (- 5, - 6) or (- 5, 10 )