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)?

2 Answers
Jun 9, 2016

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

Explanation:

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)

Jun 9, 2016

(-11,-13)

Explanation:

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.