1963 AMC 12 Problem 12

Attempt Problem 12 of the 1963 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1963 AMC 12 solutions, or check the answer key.

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12.

Three vertices of parallelogram

PQRS

are

P(-3,-2),

Q(1,-5),

R(9,1)

with

P

and

R

diagonally opposite. The sum of the coordinates of vertex

S

is:

13

12

11

10

9

The diagonals of a parallelogram bisect each other

Use the vector relation

P+R=Q+S

Since

P+R=Q+S,

\begin{aligned} S&=P+R-Q\\ &=(-3,-2)+(9,1)-(1,-5)\\ &=(5,4). \end{aligned}

The coordinate sum is

5+4=9.

Therefore, the correct answer is E.

Problem 12 in other years