Question 213979
Find the coordinates of the missing endpoint given that S is the midpoint of RT.

T(-4,3),S(-1,5)


Step 1.  Let (x,y) be the endpoint.   So the average of the x and y coordinates for the endpoints will be the midpoint.  The following steps will show this


Step 2.  The x-coordinate for the midpoint S is -1.  Then


{{{-1=(x+(-4))/2}}}


{{{(-1)=(x-4)/2}}}


{{{(-2)=x-4}}}


{{{x=2}}}



Step 2.  The y-coordinate for the midpoint S is 5.  Then


{{{5=(y+3)/2}}}


{{{5=(y+3)/2}}}


{{{10=y+3}}}


{{{y=7}}}


Step 3.  ANSWER:  So the endpoint is (2,7) 


Step 4.  As a check the other endpoint is (-4,3).  Then the midpoint is calculated as


{{{(2+(-4))/2=-1}}} so the x-coordinate of the midpoint is -1


{{{(7+3)/2=5}}} so the y-coordinate of the midpoint is 5


The midpoint is then (-1,5) which was given.  So it checks out!


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J