What's the distance between #(-4\sqrt { 2} ,6)# and #( 2\sqrt { 2} ,3)#?

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Answer 1 · 2017-07-22T02:17:42

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)(2sqrt(2)) - color(blue)(-4sqrt(2)))^2 + (color(red)(3) - color(blue)(6))^2)#

#d = sqrt((color(red)(2sqrt(2)) + color(blue)(4sqrt(2)))^2 + (color(red)(3) - color(blue)(6))^2)#

#d = sqrt((6sqrt(2))^2 + (-3)^2)#

#d = sqrt((36 * 2) + 9)#

#d = sqrt(72 + 9)#

#d = sqrt(81)#

#d = 9#