The midpoint, M, of line AB is located at (-3, 7). If A has coordinates (-1.75, 2.75), what is the length of AB?

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Answer 1 · 2017-09-26T21:51:42

See a solution process below:

First, determine the distance between the midpoint M and point A. The formula for calculating the distance between two points is:

#d = sqrt((color(red)(x_M) - color(blue)(x_A))^2 + (color(red)(y_M) - color(blue)(y_A))^2)#

Substituting the values from the points in the problem gives:

#d_(AM) = sqrt((color(red)(-3) - color(blue)(-1.75))^2 + (color(red)(7) - color(blue)(2.75))^2)#

#d_(AM) = sqrt((color(red)(-3) + color(blue)(1.75))^2 + (color(red)(7) - color(blue)(2.75))^2)#

#d_(AM) = sqrt((-1.25)^2 + 4.25^2)#

#d_(AM) = sqrt(1.5625 + 18.0625)#

#d_(AM) = sqrt(19.625)#

Because M is the midpoint of the line segment AB, it follows the distance:

#d_(AM) = d_(MB)# or #d_(AB) = 2d_(AM)#

We know #d_(AM)#

Therefore:

#d_(AB) = 2d_(AM) = 2sqrt(19.625)#