What is the distance between #(2,-6)# and #(7,4)#?

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Answer 1 · 2018-03-11T22:51:37

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

#d = sqrt((color(red)(7) - color(blue)(2))^2 + (color(red)(4) + color(blue)(6))^2)#

#d = sqrt(5^2 + 10^2)#

#d = sqrt(25 + 100)#

#d = sqrt(125)#

#d = sqrt(25 * 5)#

#d = sqrt(25)sqrt(5)#

#d = 5sqrt(5)#