Question

Explain how the distance formula can prove Pythagoras' Theorem. In your

Answer 1

Answer:

Given a triangle ABC, Pythagoras' Theorem shows that:

$c^2=a^2+b^2$

Thus,

$c = \sqrt{a^2+b^2}$

The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.

$d^2 = (x_{2} -x_{1})^2 + (y_{2} -y_{1})^2$

$d = \sqrt{(x_{2}-x_{1})^2 + (y_{2} -y_{1})^2 }$

Therefore when given the hypotenuse with endpoints at

$(x_{1}, y_{1}) and {(x_{2}, y_{2})$

We know that the third point of the right triangle will be at

$(x_{2}, y_{1})$

and that the two side lengths will be defined by the absolute values of:

$(x_{2} - x_{1}) = a$

$(y_{2} - y_{1}) = b$