What is the distance between #(4, 5)# and #(-6, -7)#?

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Answer 1 · 2018-05-28T22:03:48

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)(-6) - color(blue)(4))^2 + (color(red)(-7) - color(blue)(5))^2)#

#d = sqrt((-10)^2 + (-12)^2)#

#d = sqrt(100 + 144)#

#d = sqrt(244)#

#d = sqrt(4 * 61)#

#d = sqrt(4)sqrt(61)#

#d = 2sqrt(61)#

Or

#d ~= 15.62#