Which of the following formulas calculates the Euclidean distance between X and Y?
A) $ \sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(x_{2}-\gamma_{2}\right)^{2}+\ldots+\left(x_{n}-\gamma_{n}\right)^{2}} $
B) $ \sqrt{\left(x_{1}+\gamma_{1}\right)+\left(x_{2}+\gamma_{2}\right)+\ldots+\left(x_{n}+\gamma_{n}\right)} $
C) $ \sqrt{\left(x_{1}-\gamma_{1}\right)^{2}+\left(x_{2}-\gamma_{2}\right)^{2}+\ldots+\left(x_{n}-\gamma_{n}\right)^{2}} $
D) $ \sqrt{\left(x_{n}-\gamma_{n}\right)^{2}} $

Question

Which of the following formulas calculates the Euclidean distance between X and Y? 
A) $ \sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(x_{2}-\gamma_{2}\right)^{2}+\ldots+\left(x_{n}-\gamma_{n}\right)^{2}} $
B) $ \sqrt{\left(x_{1}+\gamma_{1}\right)+\left(x_{2}+\gamma_{2}\right)+\ldots+\left(x_{n}+\gamma_{n}\right)} $
C) $ \sqrt{\left(x_{1}-\gamma_{1}\right)^{2}+\left(x_{2}-\gamma_{2}\right)^{2}+\ldots+\left(x_{n}-\gamma_{n}\right)^{2}} $
D) $ \sqrt{\left(x_{n}-\gamma_{n}\right)^{2}} $

Quizplus · Accepted Answer

The formula for Euclidean distance between two points with n coordinates is given by
$$\sqrt{\left(x_{1}-y_{1}\right)^{2}+\left(x_{2}-y_{2}\right)^{2}+\cdots+\left(x_{n}-y_{n}\right)^{2}}$$
Here, X and Y represent two n-dimensional points, so the correct formula is
$$\sqrt{\left(x_{1}-\gamma_{1}\right)^{2}+\left(x_{2}-\gamma_{2}\right)^{2}+\ldots+\left(x_{n}-\gamma_{n}\right)^{2}}$$
which matches option C.

Which of the Following Formulas Calculates the Euclidean Distance Between (x1−x2)2+(x2−γ2)2+…+(xn−γn)2 \sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(x_{2}-\gamma_{2}\right)^{2}+\ldots+\left(x_{n}-\gamma_{n}\right)^{2}} (x1​−x2​)2+(x2​−γ2​)2+…+(xn​−γn​)2​

Which of the Following Formulas Calculates the Euclidean Distance Between $\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(x_{2}-\gamma_{2}\right)^{2}+\ldots+\left(x_{n}-\gamma_{n}\right)^{2}}$