# How do you find the missing coordinate if the 1st coordinate is (2, 3) and the midpoint is (2, 5)?

Aug 8, 2016

The point is $\left(2 , 7\right)$

#### Explanation:

The formula to find the midpoint of a line is:

M((x_1+x_2)/2 ; (y_1+y_2)/2)  and we have $M \left(2 , 5\right)$

We do not even need to do any calculation to find the $x$-value, because we notice that both points have an $x$-value of 2.

The line is therefore a vertical line and the missing endpoint will also have $x = 2$

But, to prove it:
$\frac{2 + {x}_{2}}{2} = 2 \text{ "rArr 2+x_2 = 4 " } \Rightarrow {x}_{2} = 2$

$\frac{3 + {y}_{2}}{2} = 5 \text{ "rArr 3+y_2 = 10 " } {y}_{2} = 7$

We could also have just asked the question..
"3 is halfway between 3 and what other number?"

The point is $\left(2 , 7\right)$