# A line segment on the coordinate plane has endpoints (2,4) and (4,y) and the midpoint of the segment is point (3,7), What is the value of y?

May 17, 2015

There are a few ways in which to do this sum, like for example you could use two points and find the equation of the line and then solve for $y$ at the point $\left(4 , y\right)$ or we could use the midpoint formula.
which is:

$M = \left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

Which we are given $M$ to be $\left(3 , 7\right)$

So we can put in the information we know into the formula

$\left(3 , \textcolor{red}{7}\right) = \left(\frac{2 + 4}{2} , \textcolor{red}{\frac{4 + {y}_{2}}{2}}\right)$

which we can observe that we need to solve for:

$\frac{4 + {y}_{2}}{2} = 7$

Which gives us:

$4 + {y}_{2} = 14$

${y}_{2} = 10$ which is the answer to our question.

thus our end point will be $\left(4 , \textcolor{red}{10}\right)$