# 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)?

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:
$T {M}_{x} = - 8 - - 5 = - 3$
$T {M}_{y} = - 2 - 9 = - 11$

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: $U \left(- 11 , - 13\right)$

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($\frac{- 5 + x}{2}$, $\frac{9 + y}{2}$). But M is given M(-8,-2). So, we get these eqns. :

$\frac{- 5 + x}{2}$=-8 & this gives x = -11. Similarly, y = -13.