What is the distance between #(7,-22)# and #(-1,-4)#?

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Answer 1 · 2017-09-05T19:07:30

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)(-1) - color(blue)(7))^2 + (color(red)(-4) - color(blue)(-22))^2)#

#d = sqrt((color(red)(-1) - color(blue)(7))^2 + (color(red)(-4) + color(blue)(22))^2)#

#d = sqrt((-8)^2 + 18^2)#

#d = sqrt(64 + 324)#

#d = sqrt(388)#

#d = sqrt(4 * 97)#

#d = sqrt(4)sqrt(97)#

#d = 2sqrt(97)#

Or

#d = 19.698# rounded to the nearest thousandth.