SAT1000 - P932
In the rectangular coordinate plane, the Taxicab distance from point P 1 ( x 1 , y 1 ) to P 2 ( x 2 , y 2 ) is defined as: d ( P 1 , P 2 ) = ∣ x 1 − x 2 ∣ + ∣ y 1 − y 2 ∣
Given these integer points: A 1 ( − 2 , 2 ) , A 2 ( 3 , 1 ) , A 3 ( 3 , 4 ) , A 4 ( − 2 , 3 ) , A 5 ( 4 , 5 ) , then find the integer point P ( x 0 , y 0 ) so that k = 1 ∑ 5 d ( P , A k ) has the minimum value.
Submit 2 y 0 − x 0 .
Have a look at my problem set: SAT 1000 problems
The answer is 3.
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The sum 2 ∣ x + 2 ∣ + 2 ∣ x − 3 ∣ + ∣ x − 4 ∣ attains a minimum at x = 3 . The sum ∣ y − 1 ∣ + ∣ y − 2 ∣ + ∣ y − 3 ∣ + ∣ y − 4 ∣ + ∣ y − 5 ∣ is a minimum at y = 3 . So the required answer is 3 .