Question

In the xy-plane, the points M(3,1) and

N(−1, b) are 5 units apart. Which of the

following could be the value of b?​

Answer 1

b = - 2, b = 4

Explanation:

Using the distance formula

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

with (x₁, y₁ ) = M(3, 1) and (x₂, y₂ ) = N(- 1, b)

d =
`√((-1-3)^2+(b-1)^2)`

=
`√((-4)^2+(b-1)^2)`

=
`√(16+(b-1)^2)`

Then

`√(16+(b-1)^2)` = 5 ( square both sides )

16 + (b - 1)² = 25 ( subtract 16 from both sides )

(b - 1)² = 9 ( take square root of both sides )

b - 1 = ±
`√(9)` = ± 3 ( add 1 to both sides )

b = 1 ± 3

Then

b = 1 - 3 = - 2 or b = 1 + 3 = 4