Question

fill in the blank so that the resulting statement is true.
the distance, d, between the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ in the rectangular coordinate system is $d=$
the distance, d, between the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ in the rectangular coordinate system is $d=$

Explanation:

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) in a rectangular coordinate system is derived from the Pythagorean theorem. If we consider the horizontal distance as \(|x_2 - x_1|\) and the vertical distance as \(|y_2 - y_1|\), then the distance \(d\) forms the hypotenuse of a right - triangle. By the Pythagorean theorem \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Answer:

\(\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)