How do you find the coordinates of the other endpoint of a segment with the given midpoint (-3, 7) and one endpoint of a segment (5,-1)?

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Answer 1 · 2017-04-28T21:29:12

Use the midpoint formula but solve for one of the endpoints.

The Midpoint formula is:

#x_"midpoint" = (x_"endpoint" + x_"startpoint")/2#

and

#y_"midpoint" = (y_"endpoint" + y_"startpoint")/2#

Substitute -3 for #x_"midpoint"# and 7 for #y_"midpoint"#

#-3 = (x_"endpoint" + x_"startpoint")/2#

and

#7 = (y_"endpoint" + y_"startpoint")/2#

Substitute 5 for #x_"startpoint"# and -1 for y_"startpoint":

#-3 = (x_"endpoint" + 5)/2#

and

#7 = (y_"endpoint" -1)/2#

We can solve the two equations for the endpoint:

#-6 = x_"endpoint" + 5#

and

#14 = y_"endpoint" -1#

#x_"endpoint" = -11#

and

#y_"endpoint" = 15#

The endpoint is #(-11,15)#