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 $(-11,15)$