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

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