Question

In the formula d = startroot (x 2 minus x 1) squared (y 2 minus y 1) squared endroot, how does each subtraction expression relate to the pythagorean theorem?

Answer 1

Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.

What is Pythagoras Theorem?

The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.

The formula for Pythagoras Theorem is given by,

$h^{2}=a^{2} +b^{2}$

Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.

Each Subtraction in view of Pythagoras Theorem

It is is given that,

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

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

Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.

Learn more about Pythagoras Theorem here:

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