Question

What is the distance between `(15,-4)` and `(12,14)`?

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)(12) - color(blue)(15))^2 + (color(red)(14) - color(blue)(-4))^2)`

`d = sqrt((color(red)(12) - color(blue)(15))^2 + (color(red)(14) + color(blue)(4))^2)`

`d = sqrt((-3)^2 + 18^2)`

`d = sqrt((9 + 324)`

`d = sqrt(333)`

`d = sqrt(9 xx 37)`

`d = sqrt(9)sqrt(37)`

`d = 3sqrt(37)`