Question

Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)

Answer 1

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:

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ \\ =√((8--5)^2+(-3-4)^2) \\ \\ =√((13)^2+(-7)^2) \\ \\ =√(169+49) \\ \\ =√(218) \\ \\ \approx14.7648... \end{gathered}`

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.