What is the distance between #(5, –3) # and #(9,1)#?

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Answer 1 · 2018-05-19T13:06:07

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)(9) - color(blue)(5))^2 + (color(red)(1) - color(blue)(-3))^2)#

#d = sqrt((color(red)(9) - color(blue)(5))^2 + (color(red)(1) + color(blue)(3))^2)#

#d = sqrt(4^2 + 4^2)#

#d = sqrt(16 + 16)#

#d = sqrt(32)#

Or

#d = sqrt(16 * 2)#

#d = sqrt(16)sqrt(2)#

#d = 4sqrt(2)#

Or

#d = sqrt(32) ~= 5.657#