First, draw a diagram to visualize the situation:
As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.
Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ =\sqrt{(8--5)^2+(-3-4)^2} \\ \\ =\sqrt{(13)^2+(-7)^2} \\ \\ =\sqrt{169+49} \\ \\ =\sqrt{218} \\ \\ \approx14.7648... \end{gathered}[/tex]
Therefore, the distance between the points (-5,4) and (8,-3) is: √218.
