Answer:
MN = 10
Step-by-step explanation:
To find the length of a line segment or the straight distance between two points, use the formula [tex]L = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex] , where you can substitute two points, which would be (x₁ , y₁) and (x₂ , y₂). "L" stands for length.
Choose point 1 and point 2:
Point 1: M (2, -3) x₁ = 2 y₁ = -3
Point 2: N (8, 5) x₂ = 8 y₂ = 5
Substitute the values for the variables:
[tex]L = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]L = \sqrt{(8-2)^{2}+(5-(-3))^{2}}[/tex] Solve inside each bracket first by adding
[tex]MN = \sqrt{(6)^{2}+(8)^{2}}[/tex] Square each number
[tex]MN = \sqrt{36+64}[/tex] Add the numbers
[tex]MN = \sqrt{100}[/tex] Find the square root
[tex]MN = 10[/tex] Length of the line segment
Therefore the length of the line segment MN is 10.
