How do you find the distance between #(- 9,- 9)# and #( - 54,191)#?

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Answer 1 · 2017-10-01T14:40:59

See a solution process below:

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)(-54) - color(blue)(-9))^2 + (color(red)(191) - color(blue)(-9))^2)#

#d = sqrt((color(red)(-54) + color(blue)(9))^2 + (color(red)(191) + color(blue)(9))^2)#

#d = sqrt((-45)^2 + 20^2)#

#d = sqrt(2025 + 400)#

#d = sqrt(2425)#

#d = sqrt(25 * 97)#

#d = sqrt(25)sqrt(97)#

#d = 5sqrt(97)#

If a single number is needed:

#d = 49.244# rounded to the nearest thousandth