Question

Which of the following is a true statement about the distance formula?A. The (x1,y1) and (×2,y2) can be switched in the distance formula. B. It matters which point is denoted as (×1,y1) or (×2,y2) in the distance formula. C. The distance formula finds the change in x and the change in y of the three points .D. The distance formula is not a variation of the Pythagoras theorem.

Answer 1

The formula distance for two points in the plane xy is:

`d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}`

The position of (x1,y1) and (x2,y2) can be switched without changing the result. One reason for this is that the distance form P1 to P2 is equal to the distance form P2 to P1.

It doesn't matter which point we label with the subindex 1 or 2: the distance is only function of the coordinates of the points.

The change in x and the change in y, that is, the distance in each coordinate, is squared when calculated for the distance formula.

The distance formula is a variation of the Pythagoras theorem, as it is based on a right triangle.

Answer:

The statements that are true are A and B.