How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-5,9) and midpoint M(-8,-2)?

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Answer 1 · 2016-06-09T13:55:40

The endpoint #U# lies in the same direction as the midpoint, but twice as far.

We can separate the #x# and #y# distances:
#TM_x=-8--5=-3#
#TM_y=-2-9=-11#

Now we add the same distances to the coordinates of #M#
#U_x=M_x-3=-8-3=-11#
#U_y=M_y-11=-2-11=-13#

Answer: #U(-11,-13)#

Answer 2 · 2016-06-09T14:18:50

(-11,-13)

Let the other endpoint be U(x,y).

Now, with endpoints T(-5,9) & U(x,y), the midpoint M must be M(#(-5+x)/2#, #(9+y)/2#). But M is given M(-8,-2). So, we get these eqns. :

#(-5+x)/2#=-8 & this gives x = -11. Similarly, y = -13.