# How do you find the missing coordinate if the 1st coordinate is (13,5) and the midpoint is (7, -4)?

May 28, 2016

Missing coordinate is $\left(1 , - 13\right)$

#### Explanation:

Let the second coordinate be $\left(x , y\right)$. Now the midpoint of $\left(x , y\right)$ and $\left(13 , 5\right)$ is

$\left(\frac{x + 13}{2} , \frac{y + 5}{2}\right)$. But as midpoint is given as $\left(7 , - 4\right)$

$\frac{x + 13}{2} = 7$ and $\frac{y + 5}{2} = - 4$

or $x + 13 = 7 \cdot 2 = 14$ and $y + 5 = - 4 \cdot 2 = - 8$

or $x = 14 - 13 = 1$ and $y = - 8 - 5 = - 13$

Hence, missing coordinate is $\left(1 , - 13\right)$