Alain travels on the $4 \times 7$ grid shown from point $P$ to one of the points $A, B, C, D$, or $E$. Alain can travel only right or up, and only along gridlines. To which point should Alain travel in order to travel the shortest distance?

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-026.jpg?height=263&width=377&top_left_y=1863&top_left_x=1205)
(A) $A$
(B) $B$
(C) $C$
(D) $D$
(E) $E$
To get from $P$ to $A$, Alain travels 5 units right and 4 units up, for a total distance of $5+4=9$ units. (Any path from $P$ to $A$ that only moves right and up will have this same length.) To get from $P$ to $B$, Alain travels 6 units right and 2 units up, for a total distance of 8 units. To get from $P$ to $C$, Alain travels 3 units right and 3 units up, for a total distance of 6 units. To get from $P$ to $D$, Alain travels 5 units right and 1 unit up, for a total distance of 6 units. To get from $P$ to $E$, Alain travels 1 unit right and 4 units up, for a total distance of 5 units. Therefore, the shortest path is from $P$ to $E$.

ANSWER: (E)