Question

What is the distance between `(4, 5)` and `(-6, -7)`?

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)(-6) - color(blue)(4))^2 + (color(red)(-7) - color(blue)(5))^2)`

`d = sqrt((-10)^2 + (-12)^2)`

`d = sqrt(100 + 144)`

`d = sqrt(244)`

`d = sqrt(4 * 61)`

`d = sqrt(4)sqrt(61)`

`d = 2sqrt(61)`

Or

`d ~= 15.62`