# What is the distance between two points `P_1 = (x_1,y_1)` and `P_2 = (x_2,y_2)` equal to?

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Expert Answers

Charlie Hooper | Certified Educator

The distance d between two points between `P_1 = (x_1,y_1)` and` P_2 = (x_2,y_2)` is computed using the Pythagorean Theorem.

The hypotenuse of a right triangle which has the sides `a =| x_2 -x_1|and b =| y_2 -y_1|` .

Therefore,

`d^2 = a^2 +b^2 = (x_2 -x_1)^2 +(y_2 -y_1)^2` .

Obtain the distance formula by taking square roots.

The distance between ` P_1 = (x_1,y_1)` and `P_2 = (x_2,y_2)` is equal to

`d=sqrt((x_2 -x_1)^2 +(y_2 -y_1)^2)`