Answer:
The distance between point M and point N is 13.
Step-by-step explanation:
By Analytical Geometry, we know that straight line distance between two coplanar points can be determined by the Distance Equation of a Line Segment ([tex]l_{MN}[/tex]), which is an application of the Pythagorean Theorem:
[tex]l_{MN} = \sqrt{(x_{N}-x_{M})^{2}+(y_{N}-y_{M})^{2}}[/tex] (1)
Where:
[tex]x_{M}, x_{N}[/tex] - x-Coordinates of points M and N.
[tex]y_{M}, y_{N}[/tex] - y-Coordinates of points M and N.
If we know that [tex]M(x,y) = (-6,5)[/tex] and [tex]N(x,y) = (7,5)[/tex], then the distance between point M and point N is:
[tex]l_{MN} = \sqrt{[7-(-6)]^{2}+(5-5)^{2}}[/tex]
[tex]l_{MN} = 13[/tex]
The distance between point M and point N is 13.
