How do you find the coordinates of the other endpoint of a segment with the given endpoint of a segment is (12, -8) and the midpoint is (3, 18)?

1 Answer
Alan P.
Jun 22, 2016

The other end is at (-6,44)(−6,44)

Explanation:

The vector displacement from (12,-8)(12,−8) to (3,18)(3,18) is
color(white)("XXX")vec(""(3-12,18-(-8)))= vec(""(-9,26))XXX−−−−−−−−−−−−−−−−→(3−12,18−(−8))=−−−−−−−→(−9,26)

A point twice as far away from (12,8)(12,8) (but through (3,18)(3,18)
would have a vector displacement of
color(white)("XXX")2xxvec(""(-9,26))=vec(""(-18,52))XXX2×−−−−−−−→(−9,26)=−−−−−−−−→(−18,52)
from (12,-8)(12,−8)

(12,-8)+vec(""(-18,52))=(-6,44)(12,−8)+−−−−−−−−→(−18,52)=(−6,44)

Related questions
See all questions in Midpoint Formula
Impact of this question
1639 views around the world
You can reuse this answer
Creative Commons License