# How do you find the missing coordinate if the 1st coordinate is (12, -8) and the midpoint is (3, 18)?

Apr 13, 2018

$\left(- 6 , 44\right)$

#### Explanation:

$\text{the coordinates of the midpoint are the average of the}$
$\text{coordinates of the endpoints}$

$\text{here one endpoint is } \left(12 , - 8\right)$

$\text{let the endpoint to be found } = \left(x , y\right)$

$\Rightarrow \frac{1}{2} \left(12 + x\right) = 3 \leftarrow \textcolor{b l u e}{\text{x-coordinate of midpoint}}$

$\text{multiply both sides by 2}$

$\Rightarrow 12 + x = 6 \Rightarrow x = 6 - 12 = - 6$

$\Rightarrow \frac{1}{2} \left(- 8 + y\right) = 18 \leftarrow \textcolor{b l u e}{\text{y-coordinate of midpoint}}$

$\text{multiply both sides by 2}$

$\Rightarrow - 8 + y = 36 \Rightarrow y = 36 + 8 = 44$

$\Rightarrow \text{coordinates of missing endpoint } = \left(- 6 , 44\right)$