Question

the formula used to find the straight - line distance between two points on a coordinate plane is called the ____________.
the distance formula is derived from the ____________ theorem.
the distance formula is written as (sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}), which calculates the ____________ between two points.
to find the distance between two points, you first subtract the ____________.

Explanation:

1. The formula for straight-line distance between two points is named the distance formula.
2. The distance formula comes from the Pythagorean theorem (treating the distance as the hypotenuse of a right triangle with legs as coordinate differences).
3. The given expression calculates the straight-line distance between points \((x_1,y_1)\) and \((x_2,y_2)\).
4. To apply the formula, first subtract the corresponding x-coordinates and y-coordinates to find the leg lengths of the right triangle.

Answer:

distance formula
Pythagorean
straight-line distance
x-coordinates and y-coordinates (or corresponding coordinates)