Problem 267

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Problem 267: (2012 AMC 12b, 17)

Square $PQRS$ lies in the first quadrant. Points $(3,0), (5,0), (7,0),$ and $(13,0)$ lie on lines $SP, RQ, PQ,$ and $SR$, respectively. What is the sum of the coordinates of the center of the square $PQRS$? $\textbf{(A)}\ 6\qquad$ $\textbf{(B)}\ 6.2\qquad$ $\textbf{(C)}\ 6.4\qquad$ $\textbf{(D)}\ 6.6\qquad$ $\textbf{(E)}\ 6.8$

Solution

Exercise 267: Solution

Square $PQRS$ lies in the first quadrant. Points $(6,0), (10,0), (14,0),$ and $(26,0)$ lie on lines $SP, RQ, PQ,$ and $SR$, respectively. What is the sum of the coordinates of the center of the square $PQRS$?

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