# Question #2b52a

##### 1 Answer
May 23, 2017

$\left(11 , 7\right)$

#### Explanation:

We can begin by plotting the points of the line segment $P S$. Since we know that $R$ is the midpoint of the $P S$ line segment, we can use the midpoint formula to find the coordinate of $R$

The midpoint formula: $\left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

Since we have our two coordinates of $P$ and $S$ we can substitute those values into the formula to find the coordinates of $R$

If we let, $\left(8 , 10\right) \to \left(\textcolor{b l u e}{{x}_{1}} , \textcolor{red}{{y}_{1}}\right)$ and $\left(12 , 6\right) \to \left({\textcolor{b l u e}{x}}_{2} , \textcolor{red}{{y}_{2}}\right)$ then.. .

$R = \left(\textcolor{b l u e}{\frac{8 + 12}{2}} , \textcolor{red}{\frac{10 + 6}{2}}\right) = \left(\textcolor{b l u e}{\frac{20}{2}} , \textcolor{red}{\frac{16}{2}}\right) = \left(\textcolor{b l u e}{10} , \textcolor{red}{8}\right)$

Since we now know the coordinates of $R$ and already given $S$ we can find the coordinate of $Q$ since it is the midpoint of $R S$

By the same method above...

If we let, $\left(10 , 8\right) \to \left(\textcolor{b l u e}{{x}_{1}} , \textcolor{red}{{y}_{1}}\right)$ and $\left(12 , 6\right) \to \left({\textcolor{b l u e}{x}}_{2} , \textcolor{red}{{y}_{2}}\right)$ then.. .

$Q = \left(\textcolor{b l u e}{\frac{10 + 12}{2}} , \textcolor{red}{\frac{8 + 6}{2}}\right) = \left(\textcolor{b l u e}{\frac{22}{2}} , \textcolor{red}{\frac{14}{2}}\right) = \left(\textcolor{b l u e}{11} , \textcolor{red}{7}\right)$

So the coordinate of $Q$ lies at $\left(11 , 7\right)$ which is also the midpoint of line segment $R S$

Here is a graph to provide a visual representation of what I just explained.

If the image is to small, you can check the link below to this graph: https://www.desmos.com/calculator/vtaiir6ro8