How do you find the distance between points (-7,8), (3,10)?

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Answer 1 · 2017-08-17T03:43:11

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)(3) - color(blue)(-7))^2 + (color(red)(10) - color(blue)(8))^2)#

#d = sqrt((color(red)(3) + color(blue)(7))^2 + (color(red)(10) - color(blue)(8))^2)#

#d = sqrt(10^2 + 2^2)#

#d = sqrt(100 + 4)#

#d = sqrt(104)#

#d = sqrt(4 * 26)#

#d = sqrt(4)sqrt(26)#

#d = 2sqrt(26)#

Or

#d = 2 * 5.099#

#d = 10.198# rounded to the nearest thousandth.