How do you find the midpoint of #(5 1/2, -4 1/4), (3 3/4, -1 1/4)#?

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Answer 1 · 2017-01-12T14:31:35

See the full process for finding the midpoint below:

First, convert all of the mixed fractions to improper fractions over the same common denominator:

#(((4/4xx5) + (2/2 xx 1/2))#, #((4/4 xx -4) - 1/4))# and

#(((4/4 xx 3) + 3/4)#, #((4/4 xx -1) - 1/4))#

#((20/4 + 2/4)#, #(-16/4 - 1/4))# and

#((12/4 + 3/4)#, #(-4/4 - 1/4))#

#(22/4#, #-17/4)# and #(15/4#, #-5/4)#

We can now use the midpoint formula to find the midpoint of these two points.

The formula to find the mid-point of a line segment give the two end points is:

#M = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)#

Where #M# is the midpoint and the given points are:

#color(red)((x_1, y_1))# and #color(blue)((x_2, y_2))#

Substituting the points from our problem gives:

#M = ((color(red)(22/4) + color(blue)(15/4))/2 , (color(red)(-17/4) + color(blue)(-5/4))/2)#

#M = ((37/4)/2 , (-22/4)/2)#

#M = (37/8 , -22/8)#

#M = (4 5/8, -2 6/8)#

#M = (4 5/8, -2 3/4)#