# How do you find the missing coordinate if the 1st coordinate is (5,7) and midpoint is (0,3)?

Jan 22, 2017

Hence, the other end-point is $\left(- 5 , - 1\right)$.

#### Explanation:

Let $A \left(5 , 7\right) , \mathmr{and} , B \left(x , y\right)$ be the end-points of line-segment $A B$

having mid-point $M \left(0 , 3\right)$

Then, with $A \left(5 , 7\right) \mathmr{and} B \left(x , y\right)$, mid-point $M$ has to be,

$M \left(\frac{5 + x}{2} , \frac{7 + y}{2}\right)$. But $M = M \left(0 , 3\right)$.

$\Rightarrow \frac{5 + x}{2} = 0 , \frac{7 + y}{2} = 3$

$\Rightarrow x = - 5 , y = - 1$.

Hence, the other end-point is $\left(- 5 , - 1\right)$.