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

Answer:

b = - 2, b = 4

Step-by-step 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 = $\sqrt{(-1-3)^2+(b-1)^2}$

  = $\sqrt{(-4)^2+(b-1)^2}$

  = $\sqrt{16+(b-1)^2}$

Then

$\sqrt{16+(b-1)^2}$ = 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 = ± $\sqrt{9}$ = ± 3 ( add 1 to both sides )

b = 1 ± 3

Then

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