Question

What Theorem is the Distance Formula based on? (You only need to write the name of the Theorem)

Answer 1

The distance formula as given in the image can be calculated based on the Pythagorean theorem.

The Pythagorean theorem states that the sum of the opposite square and the adjacent square equals the hypotenuse square.

In the diagram given

$\begin{gathered} Opposite=(x_2\text{-}x_1\text{)} \\ Adjacent=(y_2-y_1\text{)} \\ \text{Hypotenuse}=\text{ d} \end{gathered}$

Applying the Pythagorean theorem,

$\begin{gathered} \text{Hyp}^2=Opp^2+Adj^2 \\ d^2=(x_2\text{-}x_1)^2+(y_2-y_1)^2 \\ d=\sqrt[]{(x_2\text{-}x_1)^2+(y_2-y_1)^2} \end{gathered}$

Therefore,

The distance formula can be calculated based on the Pythagorean theorem.