Question

What is the distance between `(-12,-4)` and `(-10,15)`?

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)(-10) - color(blue)(-12))^2 + (color(red)(15) - color(blue)(-4))^2)`

`d = sqrt((color(red)(-10) + color(blue)(12))^2 + (color(red)(15) + color(blue)(4))^2)`

`d = sqrt(2^2 + 19^2)`

`d = sqrt(4 + 361)`

`d = sqrt(365)`

Or

`d = 19.105` rounded to the nearest thousandth