Answer: 13 units
Explanation
Points M and N are at locations (-8,2) and (4,-3) respectively.
Let's apply the distance formula.
[tex]M = (x_1,y_1) = (-8,2) \text{ and } N = (x_2, y_2) = (4,-3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-8-4)^2 + (2-(-3))^2}\\\\d = \sqrt{(-8-4)^2 + (2+3)^2}\\\\d = \sqrt{(-12)^2 + (5)^2}\\\\d = \sqrt{144 + 25}\\\\d = \sqrt{169}\\\\d = 13\\\\[/tex]
The distance between the two points is 13 units.
Note that a 5-12-13 right triangle forms when we introduce the point P(-8,-3). So an alternative is to use the Pythagorean theorem. In fact, the distance formula is effectively a special modification of the Pythagorean theorem.
