Question

On a coordinate plane point M is located at (-6,5) and point N is located at (7,5) what is the distance between point M and point N

Answer 1

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 ($l_{MN}$), which is an application of the Pythagorean Theorem:

$l_{MN} = \sqrt{(x_{N}-x_{M})^{2}+(y_{N}-y_{M})^{2}}$ (1)

Where:

$x_{M}, x_{N}$ - x-Coordinates of points M and N.

$y_{M}, y_{N}$ - y-Coordinates of points M and N.

If we know that $M(x,y) = (-6,5)$ and $N(x,y) = (7,5)$, then the distance between point M and point N is:

$l_{MN} = \sqrt{[7-(-6)]^{2}+(5-5)^{2}}$

$l_{MN} = 13$

The distance between point M and point N is 13.