How do you find the distance between the points (4,2), (6,-2/3)?

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Answer 1 · 2017-04-05T15:16:44

See the entire 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)(-2/3) - color(blue)(2))^2)#

#d = sqrt(2^2 + (color(red)(-2/3) - (3/3 xx color(blue)(2)))^2)#

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

#d = sqrt(4 + (-8/3)^2)#

#d = sqrt(4 + 64/9)#

#d = sqrt((9/9 xx 4) + 64/9)#

#d = sqrt(36/9 + 64/9)#

#d = sqrt((36 + 64)/9)#

#d = sqrt(100/9)#

#d = sqrt(100)/sqrt(9)#

#d = 10/3#