Option B:
The length of a line segment MN is 10.4.
Solution:
Given points are M(–7, 1) and N(3, 4).
Here, [tex]x_1=-7, y_1=1, x_2=3, y_2=4[/tex]
Distance between 2 points formula:
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]
Substitute the given values in the formula.
[tex]d=\sqrt{\left(3-(-7)\right)^{2}+\left(4-1)\right)^{2}}[/tex]
[tex]d=\sqrt{\left(3+7\right)^{2}+\left(3\right)^{2}}[/tex]
[tex]d=\sqrt{10^{2}+3^{2}}[/tex]
[tex]d=\sqrt{100+9}[/tex]
[tex]d=\sqrt{109}[/tex]
d = 10.4
Option B is the correct answer.
The length of a line segment MN is 10.4.
