Question

What is the distance between `(3,-25)` and `(2,-12)`?

Answer 1

See a solution process below:

Explanation:

The formula for calculating the distance between two points is:

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

Substituting the values from the points in the problem gives:

`d = sqrt((color(red)(2) - color(blue)(3))^2 + (color(red)(-12) - color(blue)(-25))^2)`

`d = sqrt((color(red)(2) - color(blue)(3))^2 + (color(red)(-12) + color(blue)(25))^2)`

`d = sqrt((-1)^2 + 13^2)`

`d = sqrt(1 + 169)`

`d = sqrt(170)`

`d = 13.038` rounded to the nearest thousandth.