Respuesta :
Let's say point A is (-3,4) and point B is (8,-7).
The x-distance from A to B is -3 to 8. This is equivalent to the expression [tex]\abs{8 - (-3)} = \abs{11}[/tex]. So the x-distance is 11.
The y-distance from A to B is 4 to -7. This is equivalent to the expression [tex]\abs{(-7) - 8} = \abs{-13}[/tex]. So the y-distance is 13. We take the absolute value because distance is always positive, and is never negative.
The x- and y-distances create a right triangle. So, we can apply the Pythagoren Theorem: [tex]a^{2}+b^{2}=c^{2}[/tex], where [tex]a[/tex] and [tex]b[/tex] are the shorter sides, and [tex]c[/tex] is the longer side of the triangle.
the x- and y-distances are [tex]a[/tex] and [tex]b[/tex]. We want to find the value of c, since that is the distance between the two points. So, plugging the known values into the Pythagorean Theorem,
[tex]11^{2}+13^{2}=c^{2}[/tex]
[tex]121+169=c^{2}[/tex]
[tex]290=c^{2}[/tex]
[tex]c\approx 16.1245154966 [/tex]
So, the distance between the two points is roughly 16.
