What is the distance between #(31,-201)# and #(28,-209)#?

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Answer 1 · 2017-07-23T12:49:26

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)(28) - color(blue)(31))^2 + (color(red)(-209) - color(blue)(-201))^2)#

#d = sqrt((color(red)(28) - color(blue)(31))^2 + (color(red)(-209) + color(blue)(201))^2)#

#d = sqrt((-3)^2 + (-8)^2)#

#d = sqrt(9 + 64)#

#d = sqrt(73)#

Or

#d = 8.544# rounded to the nearest thousandth.

Answer 2 · 2017-07-23T17:28:03

#color(blue)(8.544#

#:.y-y=(-201)-(-209)=8=opposite#

#:.x-x=31-28=3=adjacent#

#:.8/3=tantheta=2.666666667=69°26'38''#

hypotenuse=distance

Distance#:.=sectheta xx 3#

Distance#:.=sec69°26'38'' xx 3#

Distance#:.=2.848001248 xx 3=8.544003745#

#:.color(blue)(=8.544# to 3 decimals