Step-by-step explanation:
Let's say we have a right triangle with vertices at A(0,0), B(10,0), and C(10,10).
As you can see, the triangle has side lengths of 10 and 10.
Let's now find the distance of the hypotenuse.
AC = [tex]\sqrt{10^2+10^2}[/tex]
As you can see, this provides us the distance of the hypotenuse, or the line segment AC.
If we look at AC closer, we notice that AC is represented by points on the coordinate plane.
Now, try finding the distance between points A and C using the distance formula.
Distance = [tex]\sqrt{(10-0)^2+(10-0)^2}[/tex]
Distance = [tex]\sqrt{10^2+10^2}[/tex]
As this is the same as AC, we can say that we have now derived the distance formula from the Pythagorean theorem.