Question

relationship between distance formula and pythagorean theorem

Answer 1

the distance between two points in two-dimensional space:

point 1 (x1, y1)
point 2 (x2, y2)

you can use the pythagorean theorem to compute the distance:

distance^2 = (x2 - x1)^2 + (y2 - y1)^2

so distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Answer 2

http://www.purplemath.com/modules/distform.htm

has some pictures to go with the above explanation.

Answer 3

the lengths that you take to go the distance are the same.

Answer 4

the length of the hypotenuse of a right triangle is the distance from one point to the other. A hypot has a slant to it, a slope, a lean. Slope is determined by the difference in the heights of the 2 points as a ratio to how for out it goes.