119k views
5 votes
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?​

User Mvanella
by
8.8k points

1 Answer

5 votes

Answer:

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

User Hugot
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories