Point $R$ is the midpoint of the line segment $P Q$ and $S$ is the midpoint of the line segment $Q R$. If $P$ has coordinates $(2,1)$ and $S$ has coordinates $(14,7)$, then the coordinates of $Q$ are
(A) $(8,4)$
(B) $(26,13)$
(C) $(10,5)$
(D) $(18,9)$
(E) $(16,11)$

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-117.jpg?height=404&width=612&top_left_y=1609&top_left_x=1193)
Since $R$ is the midpoint of $P Q$ and $S$ is the midpoint of $Q R$, then $S$ is $\frac{3}{4}$ of the way from $P$ to $Q$.

Since $S$ is 12 units to the right of $P$, then $Q$ is $\frac{4}{3} \times 12=16$ units to the right of $P$. Since $S$ is 6 units up from $P$, then $Q$ is $\frac{4}{3} \times 6=8$ units up from $P$.

Therefore, the coordinates of $S$ are $(2+16,1+8)=(18,9)$.

![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-230.jpg?height=469&width=658&top_left_y=248&top_left_x=1189)

Answer: (D)